BayesiaLab User Guide

BayesiaLab User Guide

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BayesiaLab User GuideBayesia

BayesiaLab User GuideBayesiaCopyright © 2001-2010 Bayesia SAS

Table of ContentsWelcome ..................................................................................................................................... vIntroduction ................................................................................................................................ viI. Main window ............................................................................................................................ 1II. Graph Windows ....................................................................................................................... 2

1. Status Bar ....................................................................................................................... 21.1. Database Report ................................................................................................... 6

2. Information panel ........................................................................................................... 103. Graph panel ................................................................................................................... 12

3.1. Graph panel use ................................................................................................. 123.2. Node Management .............................................................................................. 143.3. Node Edition ....................................................................................................... 16

3.3.1. Discrete Node .......................................................................................... 233.3.2. Continuous Node ...................................................................................... 253.3.3. Conditional Probability Table ...................................................................... 303.3.4. Deterministic nodes .................................................................................. 323.3.5. Equations ................................................................................................ 333.3.6. Assessments ........................................................................................... 63

3.4. Node States ........................................................................................................ 693.5. Constraint node ................................................................................................... 723.6. Utility node .......................................................................................................... 733.7. Decision node ..................................................................................................... 743.8. Arc Management ................................................................................................. 753.9. Arc states ........................................................................................................... 773.10. Filtered States ................................................................................................... 803.11. Class management ............................................................................................ 823.12. Constant management ....................................................................................... 853.13. Cost Management ............................................................................................. 873.14. Forbidden arc management ............................................................................... 883.15. Temporal Indices ............................................................................................... 903.16. Structural Complexity Influence Coefficient .......................................................... 913.17. Local Structural Coefficients ............................................................................... 923.18. State Virtual Numbers ........................................................................................ 933.19. Experts ............................................................................................................. 94

3.19.1. Assessment Report ................................................................................ 963.20. Variations .......................................................................................................... 993.21. Comments ...................................................................................................... 1003.22. Contextual menus ............................................................................................ 104

4. Monitor panel ............................................................................................................... 1094.1. Monitor use ....................................................................................................... 1094.2. Monitor contextual menus .................................................................................. 120

5. Shortcuts ..................................................................................................................... 122III. Menus ................................................................................................................................ 125

1. Network ....................................................................................................................... 1251.1. Network export .................................................................................................. 1271.2. Network Locking ................................................................................................ 129

2. Data ............................................................................................................................ 1312.1. Data Importation Wizard .................................................................................... 1372.2. Data Association Wizard .................................................................................... 1542.3. Evidence Scenario File ...................................................................................... 1602.4. Graphs ............................................................................................................. 163

2.4.1. Bar chart ................................................................................................ 1632.4.2. Occurrence matrix .................................................................................. 1652.4.3. Distribution function ................................................................................ 1662.4.4. Scatter of points (2D) .............................................................................. 1682.4.5. Colored Line Plot .................................................................................... 170

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2.4.6. Scatter of points (3D) .............................................................................. 1722.4.7. Bubble chart ........................................................................................... 174

3. Edit ............................................................................................................................. 1774. View ............................................................................................................................ 1795. Learning ...................................................................................................................... 181

5.1. Association Discovering ..................................................................................... 1825.2. Characterization of the target node ..................................................................... 1875.3. Clustering ......................................................................................................... 1925.4. KMeans Clustering ............................................................................................ 1965.5. Multiple clustering .............................................................................................. 1975.6. Policy learning of Static Bayesian networks ......................................................... 2005.7. Policy Learning of Dynamic Bayesian networks ................................................... 201

6. Inference ..................................................................................................................... 2026.1. Adaptive Questionnaire ...................................................................................... 2036.2. Interactive inference .......................................................................................... 2066.3. Interactive Bayesian updating ............................................................................. 2086.4. Batch labeling ................................................................................................... 2126.5. Batch inference ................................................................................................. 2146.6. Batch most probable explanation labeling ........................................................... 2166.7. Batch most probable explanation inference ......................................................... 2186.8. Batch joint probability ......................................................................................... 2206.9. Batch Likelihood ................................................................................................ 222

7. Analysis ....................................................................................................................... 2247.1. Graphical analysis ............................................................................................. 2247.2. Analysis reports ................................................................................................ 2537.3. Network Performance ........................................................................................ 271

7.3.1. Network Targeted Performance ................................................................ 2717.3.2. Network global performance (Log-likelihood) ............................................ 281

7.4. Target Optimization ............................................................................................ 2897.5. Target Optimization Tree .................................................................................... 2917.6. Target Interpretation Tree ................................................................................... 298

8. Monitor ........................................................................................................................ 3039. Tools ........................................................................................................................... 305

9.1. Network Comparison ......................................................................................... 3059.1.1. Graphical Structure Comparator .............................................................. 3089.1.2. Comparison of Joint Probabilities ............................................................. 311

9.2. Arc Confidence ................................................................................................. 3189.2.1. Data Perturbation ................................................................................... 3209.2.2. Targeted Cross Validation ........................................................................ 3239.2.3. Structural Coefficient Analysis ................................................................. 3289.2.4. Network Extraction ................................................................................. 333

9.3. Multi-Quadrant Analysis ..................................................................................... 33510. Dynamic Bayesian networks ....................................................................................... 341

10.1. Time variable ................................................................................................... 34411. Options ...................................................................................................................... 346

11.1. Settings .......................................................................................................... 34612. Help .......................................................................................................................... 361

12.1. Analysis of the use of BayesiaLab ..................................................................... 361IV. Toolbars .............................................................................................................................. 365V. Search ................................................................................................................................ 370VI. Console ............................................................................................................................. 373

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BayesiaLab User Guide

WelcomeWelcome in the BayesiaLab Help document.

BayesiaLab is a complete tool for the creation and the use of Bayesian networks.

Documentation

BayesiaLab integrates Help under the JavaHelp format.

This Help document describes the functionalities and the BayesiaLab user interface.

When you are using BayesiaLab, you can press to display the help.

Pressing will display the contextual help cursor.

Once this mode is enabled, you can click on every component (menus and submenus as well) to displaya specific contextual help.

About JavaHelp

JavaHelp is a cross-platform help system developed by Sun Microsystems to be the Help tool for theJava applications and for the applets.

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IntroductionBayesian networks are represented by graphical structures (nodes and arcs). Nodes correspond torandom variables and arcs correspond to direct probabilistic relations between these connected variables.These probabilistic relations are quantified by means of probability distributions (usually a conditionalprobability table associated to the nodes).

Bayesian networks can be automatically learned from databases and/or manually modeled by experts.It is then possible to update the probability distribution of each variable by taking into account the stateof other variables.

BayesiaLab is a tool for graphical manipulation of Bayesian networks. It allows defining, modifying, usingand learning models based on Bayesian networks.

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Chapter I. Main window

The main window is the BayesiaLab work environment. It is divided into 3 main parts:

1. the command zone (menus and toolbar) that contains all the commands that can operate either onall the graphs, or on the active graph.

2. the graph zone in which graph windows are opened. The minimum contextual menu, activated byright clicking on the zone of graphs, allows managing the display of the console.

3. the graph bar that allows handling the graphs windows. A left click on the network name button makesthe corresponding graph active. The contextual menu (right click) of this bar makes it possible reor-ganizing the graph windows (Cascade/Horizontal and vertical Mosaics and Reduction).

The contextual menu of a network name button allows acting on the state of the graph window(Maximize/Minimize/Icon/Close and Rename).

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Chapter II. Graph WindowsThe graph windows are windows encapsulating independent data sets. Data included in a graph are ofseveral types :

• Qualitative data: the structure of the graph (Nodes and Arcs),

• Quantitative information: Conditional Probability Table and Databases.

A graph window can be in two different modes and two buttons allow switching from one mode to theother one.

1. Modeling Mode : mode where the graph visualization panel is visible and in which actions ofmodeling and learning are carried out.

2. Validation Mode : mode where the graph visualization panel and the monitor visualizationpanel are visible and in which actions of validation and exploitation are carried out.

1. Status Bar

The status bar of a graph window (lower part of the window) is made up of several elements :

Mode buttons

A graph window can be in two different modes. The following two buttons are used to pass from onemode to the other one.

• To switch to Modeling mode

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• To switch to Validation mode. Switching to this mode can require a series of blocking tasks dueto the computation of node probabilities and to the inference options.

Task progress bar

During some data processing (learning, inference, automatic positioning of the nodes, analysis, etc),the task in progress blocks some functionalities of this graph window.

The task progress bar thus has three states :

• when the system is ready

• when a task is in progress. The bar represents an indication of the time spent (notethat time evolution is not necessarily linear or even growing). A click on the red light stops the progressof the task.

• when a task is stopped.The button becomes orange while the process ends. It allowsthe network to go back to a correct state after having stopped the current task. At this time, the buttonis no more clickable until it turns green.

Selection counters

An indicator displays the number of selected nodes and the number of selected arcs : . The nodecount is on the left and the arc count is on the right.

Structural complexity influence coefficient

When the structural complexity influence coefficient used during learning is different from 1, the icon ofthe coefficient indicator is displayed in the status bar: . A click on this icon opens the editor of thestructural complexity influence coefficient.

Cost indicator

When costs different from 1 are associated to the nodes in the network, the icon of the cost indicator isdisplayed in the status bar: . A click on this icon opens the cost editor dialog.

Class indicator

When classes are defined in the network, the icon of the class indicator is displayed in the status bar:. A click on the icon opens the class editor dialog. A right click on the icon displays the list of the

classes. If a class is selected, it will be displayed and if deselected, it will be hidden.

The checkbox named All is a short-cut to select or unselect all the checkboxes at the same time. Whena class is not checked, the nodes that are part of it become transparent and not selectable anymore. Ifan arc is between two transparent nodes, it becomes transparent also.

Note that when an arc or a node is transparent, whatever the reason, it is not selectable anymore.

The checkbox Intersection displays only the nodes contained in all the selected classes.

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Forbidden arc indicator

When forbidden arcs are defined in the network, the icon of the forbidden arc indicator is displayed inthe status bar: . A click on the icon opens the forbidden arc editor dialog.

Temporal indices indicator

When temporal indices are associated to nodes, the icon of the temporal indices indicator is displayedin the status bar: . A click on the icon opens the temporal indices editor.

Constant indicator

When constants are defined in the network, the icon of the constant indicator is displayed in the statusbar: . A click on the icon opens the constant editor dialog.This icon is only accessible in the modelingmode.

Filtered states indicator

When some nodes have a filtered state, the icon of the filtered state use indicator is displayed in thestatus bar: . A click on the icon proposes to remove all the filtered states.

State virtual number indicator

When a node has a virtual number of states, the icon of the state virtual number use indicator is displayedin the status bar: . A click on the icon opens the state virtual number editor.

Local structural coefficient indicator

When a node has a structural coefficient, the icon of the structural coefficient use indicator is displayedin the status bar: . A click on the icon opens the local structural coefficient editor.

Experts Indicator

When experts are associated with the network, the icon of the expert use indicator is displayed in thestatus bar: . A click on the icon opens the Expert Editor of the network.

A right click on the icon displays a menu that allows the user to display the assessment report.

Temporal indicator

When we want to use the time as a variable (named: ?t?) in the formulas describing the probability dis-tributions, the icon of the temporal indicator is displayed in the status bar: . A click on the icon allowsremoving the use of the time variable in the network. In this case, the nodes using the time variable intheir formulas will be displayed with the icon: . This icon is only accessible in the modeling mode.

Scenario file

When an evidence scenario file was imported or manually created in validating mode, the icon isdisplayed in the status bar. A click on this icon allows us to remove the evidence file associated to thenetwork.

The tooltip of the icon displays the number of scenarios contained in the file.

In validation mode, a right-click on the icon displays a list of the evidence sets contained in the file. Aclick on a line sets the corresponding observations and the associated comment is displayed in thestatus bar, if it exists.

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Virtual database

It is possible to learn a Bayesian network considering an initial structure. To take into account this apriori knowledge, we consider a virtual database with N samples, where N corresponds to the numberof cases that have been used to set this a priori knowledge.The distribution of these samples correspondsto the joint probability distribution represented by the initial Bayesian network. This virtual database andthe real database are then both taken into account by the learning algorithms to induce a new Bayesiannetwork. The icon at the right-hand side of the bar is displayed. A click on this icon removes the as-sociation between the network and the virtual database.

Associated database

When the Bayesian network has an associated database, the icon at the right-hand side of the bar isactivated: . Pointing on the icon displays a tooltip containing the complete path of the associateddatabase, the number of examples contained in the database, the number of rows used for learning andfor the tests if it was defined, and if the database contains weights of missing values. A click on this iconremoves the association between the network and the database. When the database contains missingvalues, a question mark is added to the database icon: . When the database has a weight variable,a new symbol is added to the database icon to indicate it: . When the database contains rows usedfor learning and rows used for tests, the following symbol is added to the icon: . If the database isstratified, another symbol is added: . Finally, the icon can look like this: .

The tooltip associated to the icon shows, according to the case:

• the name of the database or if it is an internal database,

• the total number of examples,

• the learning examples number,

• the test examples number,

• the sum of the weights,

• the stratification over a node and the corresponding probability distribution,

• the presence of missing values.

A right click on the icon displays a menu that allows the user to:

• remove the data type (test, learning),

• remove the database stratification,

• remove the weights,

• display the database report.

In validation mode, if the database has row identifiers, a + right-click on the icon displays a floatingpanel allowing the user to perform a search among the identifiers. The search is done thanks to a textfield. The wildcards characters ? and * can be used. ? can replace one and only one character. * can

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replace none or several characters. The Case Sensitive option allows the search to respect the case.After pressing enter, the search is performed and the list of the results is displayed. The number of cor-responding rows is displayed at the bottom of the panel. A click on a line sets the corresponding obser-vations and the row identifier is displayed in the status bar:

Lock indicator

It is possible to lock the editing of a network to use it only in validating mode.When the network is locked,the icon is displayed in the status bar. By clicking on this icon, the user can enter its password tounlock the network. Then, the icon is displayed in the status bar. When the network is unlocked, aclick on the icon locks it immediately. The lock manager, which can be accessed from the Networkmenu, allows adding a lock, removing a lock, changing the password of the lock, etc.

1.1. Database Report

This report is generated from the contextual menu of the database icon in the status bar.

It contains two parts. The first part is a global summary analysis of the database:

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It shows the number of variables, the number of variables with missing values and the number of variableswith continuous values associated.

The global database is analyzed and the number of examples is indicated. If the database has stratific-ation on a node, it is also indicated with the corresponding probability distribution. The sum of weightsand the normalization factor of the weights are displayed if database has associated weights.The reportindicates the number of missing values and if the database has row identifers.

If the database has data types associated, the learning and test databases are also analyzed. For eachone, the example number, the sum of the weights and the number of missing values are shown.

The second part of the report details the content of the database for each variable:

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For each discrete or continuous variable, the numbers of missing values and filtered values with theirassociated percentages are displayed if necessary. For the continuous variables, the report indicates ifthey have associated continuous values. It indicates also the minimum, the maximum and the mean ofeach continuous variable.

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All this information is displayed for the global, learning and test databases if data types are associated.

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2. Information panel

The information panel of a graph window is visible only in Validation mode. It can be closed or openedwith the button located at the bottom right of the panel. It contains up to six different data:

Joint Probability

The joint probability corresponds to the current set of observations done (hard positive and negativeevidence, and soft evidence). Without evidence, this joint probability is obviously equal to 100%. It isautomatically updated at each modification of the monitors.

Log-Likelihood

The Log-Likelihood is the log2 of the joint probability. When the joint probability equals 100%, its valueis 0. It tends towards the infinity when the joint probability tends towards 0. It is automatically updatedat each modification of the monitors.

Cases

When a database is associated with the network, the information panel contains an estimation of thenumber of records that correspond to the current evidences (hard positive and negative evidences, andsoft evidence). Without any evidence, the number of records is obviously equal to the database size. Itis automatically updated at each modification of the monitors.

Total value

When there is at least a node with associated values in the Bayesian network, the expected total valueof the network is displayed in the information panel.

Mean value

When there is at least a node with associated values, the expected mean value of the nodes havingassociated values is displayed in the information panel.

Uncertainty

This value represents the uncertainty variations over the unobserved nodes relatively to the fully discon-nected network.This value is computed from the entropy (the highest entropy corresponds to the uniformdistributions and the lowest one to a probability of 100% on a state). This value is computed only if thecorresponding option is checked in the monitor panel's contextual menu.

Likelihood

This value represents the likelihood variations of the Bayesian network relatively to the fully disconnectednetwork. This likelihood is computed from the joint probabilities of the evidences done. This value iscomputed only if the corresponding option is checked in the monitor panel's contextual menu.

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A tooltip displays all the previous values but without rounding them.

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3. Graph panel

In Modeling mode, a graph window only presents the visualization panel of the graphs. In this paneland this mode, it is possible to build and modify a Bayesian network manually or by learning.

3.1. Graph panel use

The visualization panel allows modeling and inspecting the structure of the network.

A network is made of variables represented by nodes and relations between its variables representedby arcs. This panel makes it possible to graphically create, remove, and modify these objects.

Lastly, after associating to each node a probabilistic representation, this panel also allows accessingthe visualization and the modification of the probability distributions.

In order to contribute to the modification of the graph structure, the visualization panel can be in one ofthe following modes, selected thanks to the tool bar:

selection mode: in this state, a click on a node or an arc selects the object (see states of a nodeand states of an arc). A "drag and drop" on a selected node makes moving all the selected nodes.Lastly, a click on the graph background makes it possible to initiate the definition of a selection zone.

node creation mode: in this state, a click on the graph background creates a new node namedautomatically. At the same time, a minimum probability table is created and associated to this node.Thenew node is binary, without a priori probabilities.

constraint node creation mode: in this state, a click on the graph background creates a new con-straint node named automatically.

utility node creation mode: in this state, a click on the graph background creates a new utility nodenamed automatically.

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decision node creation mode: in this state, a click on the graph background creates a new decisionnode named automatically.

arc creation mode: in this state, a click on a node followed by a drag towards another node createsan arc between these two nodes, only if this arc does not introduce any loop.

deletion mode: in this mode, a click on an object (arc or node) deletes it. A click on the graph back-ground allows initiating the definition of a deletion zone.

By default, a right click allows to come back into selection mode. However, it is possible to change thisbehavior to come back in selection mode automatically after any action. This behavior can be modifiedthrough the preferences.

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3.2. Node Management

The creation of a node is made either in the creation mode (see Use) or by using the shortcut +click.

Constraint Node Creation

The creation of a constraint node is made either in the creation mode (see Use) or by using the shortcut + click.

Utility Node Creation

The creation of a utility node is made either in the creation mode (see Use) or by using the shortcut +click.

Decision Node Creation

The creation of a decision node is made either in the creation mode (see Use) or by using the short-cut + click.

Target Node Creation

A target node and a target state are created with the contextual menu associated to the node.

Hidden Node Creation

The creation of a hidden node is made when creating a node while a database is associated with thenetwork.

Node Deletion

The deletion of the node is made either in the deletion mode (see Use) or by using the shortcut +click.

Node Moving

The moving of a node is made either in the selection mode (see Use) or by using the shortcut +click.Automatic tools for node positioning can be used to layout the nodes while trying to satisfycontradictory constraints (to move away the nodes, to decrease the size of the arcs, etc).

Node Edition

The node edition dialog box allows to change the type of the node, to create/delete/change states, andto edit the probabilities. This dialog box is activated by the contextual menu that is associated with thenode, or by double-clicking on the node. The name of the node can be directly changed by double-clicking on it.

Node Monitoring

In Validation mode, the contextual menu associated to a node allows creating a monitor.

Temporally Spied Node

In the case of dynamic Bayesian networks, it is possible to spy the probability evolution of a node value.The setting of the value (or the cancellation) is done by using the node contextual menu.

Node Exclusion

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Excluding a node allows us to not take it into account during learning. Excluding a node can be donethrough the node contextual menu, or with the shortcut + double-click.

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3.3. Node Edition

A node represents a discrete or a discretized variable. In this last case, the modeled variable is continuousand thresholds were defined either automatically or manually, in order to associate a discrete state toany continuous value.

A node has at least two values (also named states or states) with an associated probability distributionfor each combination of the values of its parents.

A node is edited by using the dialog box illustrated on the screenshot below. In that example, the editednode is the discrete node Dyspnea, which has two values (Yes and No). As this node has two binaryparents, there are four probability distributions describing the probabilistic relation between Dyspneaand its two parents, TbOrCa and Bronchitis.

This dialog box is made of two main areas:

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• The top area containing the name of the node currently edited. The associated combo box allowschanging the node to edit. The "Rename" button allows renaming the current node. It displays thefollowing dialog box:

Note that the renaming of a node is simply done by double-clicking on the node name on the graph.

• The area with thumbnails that allow selecting the different properties to modify. There are seven dif-ferent thumbnails:

States

The States panel contains two areas:

• The area containing the type of the variable/node being edited. Two types are available:

• Discrete: for the discrete variables

• Continuous: for the discretized variables with continuous numerical values.

• The states list edition panel and the associated buttons. A node has at least two states.

Probabilities distribution

This panel allows editing the probabilities associated with the node. It contains two areas:

• The View Mode area that allows displaying and editing the table of conditional probabilities inthree forms:

• probabilistic

• determinist

• equations

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• When a database is associated to the network, a third button is available:

As illustrated above, this button replaces the Conditional Probability Table by the correspondingoccurrence matrix, taking into account the smoothing factor, if any.

• The conditional probability table edition area that allows modifying the probabilities associated tothe node. It is possible to change the order of the parents by clicking and dragging the name of theparent in the header of the table's left part. Once a parent is reordered, the modifications arepropagated in the conditional probability table.

• When experts are associated with the network, a button Assessment is displayed and is activatedwhen a cell is selected. The border of the cells with assessments becomes green and the icon

displayed in the cell indicates how important is the disagreement between the experts for this cell.

Properties

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This panel allows editing four properties of the node. The edition of each property is also available fromthe node's contextual menu.

• The color: allows displaying a colored tag on the node, its comment and its monitor. Checking theoption or clicking on the preview rectangle allows displaying the color chooser dialog box. Once thecolor selected, it is displayed inside the rectangle and can be modified again by clicking on the rectangle.To remove the color, you will have to uncheck the option. The Propagate color to the classes buttondisplays a dialog box allowing selecting the classes, associated to the node, on which we want topropagate the color. In this case, all the nodes belonging to these chosen classes will display thesame selected color or any if there is no selection.

• The image: allows displaying an image instead of the node's default representation. Checking theoption or clicking on the preview rectangle allows displaying the file chooser dialog box in order tochoose the wanted image. The display size is 30*30. If an image is bigger, it will be reduced, if it issmaller, it will be centered. The image will be saved in the network's file. To remove the image, youwill have to uncheck the option. The Propagate image to the classes button displays a dialog boxallowing selecting the classes, associated to the node, on which we want to propagate the image. Inthis case, all the nodes belonging to these chosen classes will display the same selected image orany if there is no selection.

• The temporal index: allows associating a temporal index to the node. This index is a positive or nullinteger. It allows indicating a temporal order between the nodes that is taken into account by thelearning algorithms. A node with a temporal index greater than the temporal index of another nodecannot be its ancestor.To remove the index, you will have to uncheck the option.The Propagate indexto the classes button displays a dialog box allowing selecting the classes, associated to the node,on which we want to propagate the index. In this case, all the nodes belonging to these chosen classeswill have the same index or any if there is no index.

• The cost: allows associating a cost to the node.This cost is a real superior or equal to 1 representingthe cost of an observation upon a node.The cost is used in the adaptive questionnaire. It is possibleto make a node not observable by unchecking the option. In this case, the node will not be proposedin the adaptive questionnaire. It is also possible to use the "not observable" cost to ignore the valuesof the node that are read in a database (cf. Interactive inference, Batch labeling, Batch jointprobability), to indicate the node to update (cf Interactive Bayesian updating), or to indicate the

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node for which one wants to compute the posterior probability distribution for each case described ina database (cf Batch inference). The Propagate cost to the classes button displays a dialog boxallowing selecting the classes, associated to the node, on which we want to propagate the cost. Inthis case, all the nodes belonging to these chosen classes will have the same cost or will be not ob-servable if there is no cost.

• The state virtual number: allows replacing the real number of states during the learning with theMDL score. The node's state number has an important impact on the MDL score computed duringthe structural learning. This allows influencing the network's structural complexity locally to the node.More a node has states the less it has chance of having linked parents during the learning and viceversa. Decreasing this parameter decreases the MDL score of the node and vice versa. ThePropagate state virtual number button displays a dialog box allowing selecting the classes, associ-ated to the node, on which we want to propagate the state virtual number. In this case, all the nodesbelonging to these chosen classes will have the same state virtual number or any if there is no one.

• The local structural coefficient: this parameter acts like the network's global structural coeffi-cient but is proper to each node. It can increase or decrease the structural complexity of the networkat the node. This parameter acts on the whole MDL score of the node contrary to the state virtualnumber. More a node has a high MDL score the less it has chance of having linked parents duringlearning and vice versa. Decreasing this parameter decreases the node's MDL score and vice versa.The Propagate local structural coefficient button displays a dialog box allowing selecting theclasses, associated to the node, on which we want to propagate the local structural coefficient. Inthis case, all the nodes belonging to these chosen classes will have the same local structural coefficientor any if there is no one.

• The exclusion: a node can be excluded during structural learning, meaning the learning algorithmwon't add any arc having this node as extremity. This is particularly useful if you wish to learn thestructure of a network on a subset of nodes. The Propagate exclusion button displays a dialog boxallowing selecting the classes, associated to the node, on which we want to propagate the exclusionstatus. In this case, all the nodes belonging to these chosen classes will have been excluded or not.

Classes

This panel allows managing the classes associated to the node. A class is defined as a set of nodes ofa network with an associated name. The concept of classes allows to regroup nodes having commonproperties and to manage globally these properties. A node can belong to several classes at the sametime. The classes can be also managed with the class editor.

The left list contains classes to which the node belongs. The buttons allows adding a class that alreadyexists in the network, to add a new class that does not exist in the network and to delete the selectedclasses.

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Values

This panel allows managing the values associated to the node's states. We can associate a numericalvalue to each state of the node. These values allow computing an expected numerical value for thesenodes, even if these nodes are purely symbolic. It is also possible not to assign a value to certain states.The states without associated value are then excluded from the calculation of the expected value.

The values are used quite like Utility nodes. Indeed, an expected numerical value can be obtained byassociating an Utility node to each node, except that the states without values cannot be representedwith this kind of node. Thus, these values are used to evaluate the network, to measure the impact ofsuch lever on the quality of the network. However, unlike Utility nodes, these values are not taken inaccount during the action policies learning. On the other hand, the values are used in the Pearson'slinear correlation coefficient.

When the node is continuous and has associated data, a button Generate Values is displayed at thebottom and allows computing automatically the values associated to the sates from the database.Weightsare taken into account.

State names

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This panel allows managing the long names associated to the node's states. We can associate a longname to each state of the node.These long names can be used in the monitors, reports and during dataexport as well (saving database, imputation).

Filtered State

This panel allows us to specify if there is or not a filtered state. Only one filtered state is allowed byvariable, continuous or discrete. This state is used to represent the cases where the variable does nothave a real existence like, for example, an analysis which would be made according to the positiveresult of a test.

Comment

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The last panel allows editing the comment associated to the node.This comment is in HTML. It is possibleto add hypertext links, images and to modify the background and foreground colors. The fonts are fullycustomizable. A complete description of the integrated HTML editor is available. The comment editionis also available from the node's contextual menu.

3.3.1. Discrete Node

Discrete nodes are discrete variables that can be symbolic or numerical.

There are three kinds of discrete nodes:

1. Discrete nodes with symbolic values (here a Boolean) :

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2. Discrete nodes with integer values:

3. Discrete nodes with real values:

The button "Generate states" opens the following windows:

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It is then possible to set the desired number of states. The automatic naming prefixes all the states withan L and associates the rank of the state. With the numbered names, it is possible to change the stringprefix. In the first two cases, the variable is symbolic. A numerical variable is defined by using integeror real labels. It is possible to automatically generate a sequence of integers by specifying the startingvalue and the step. In the same manner, it is possible to give real values by indicating the starting valueand the step.

The button "Generate names" allows launching the automatic naming that use the L prefix.

The button "Aggregates" allows running the aggregate editor. This one allows adding or removing, forthe selected state, different names considered equivalent (aliases). It is useful when you need to asso-ciate a database with a network. It is possible to rename directly an aggregate by double-clicking on itsname in the table.

By clicking on the "Add" button, a new dialog box is displayed allowing entering a new aggregate name:

The buttons "Up" and "Down" allow changing the order of the states. The modification of this order ispropagated into the conditional probability tables, in the long state names and in the values associatedto the states. Once the modification of the node is validated, the new order is propagated on the prob-ability tables of the children nodes of the current node.

3.3.2. Continuous Node

Continuous nodes correspond to discretized continuous variables.The discretization needs the definitionof thresholds that allow associating a set of continuous values to a discrete state. The thresholds can

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be manually set and/or automatically learned. If data are associated to this node then the button Curveallows displaying the interface for automatic and manual discretization from data.

A state of a discretized variable is composed of three fields:

• a label,

• the lower bound,

• the upper bound.

The modification of the intervals can be done by four ways:

1. via the interval chart (colored zone):

• a left click allows moving the threshold along the axis.

2. via the table. The manual data entry must respect the following constraints:

• the lower bound must be lower or equal to the upper one and higher than the upper bounds of thepreceding states;

• the upper bound must be higher or equal to the lower bound and lower than the lower bounds ofthe following states;

3. with the button "Normalize" that computes intervals of equal width;

4. with the button "Generate Intervals" that opens the following window:

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It is possible to set the number of desired intervals as well as the global lower and upper bounds. Adiscretization with equal width is then performed between these global bounds and the labels arenamed with the following syntax <=lower bound and >upper bound when using the automaticnaming, or prefixed by a string followed by the order number of the label.

The button "Generate Names" allows launching the automatic naming using <=lower bound and>upper bound.

The button "Aggregates" allows running the aggregate editor. This one allows adding or removing, forthe selected state, different names considered equivalent (aliases). It is useful when you need to asso-ciate a database with a network. It is possible to rename directly an aggregate by double-clicking on itsname in the table.

By clicking on the "Add" button, a new dialog box is displayed allowing entering a new aggregate name:

By clicking on the "Curve" at the top of the panel, the discretization from data interface is displayed.This button is displayed only if data are associated to this node:

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This interface is similar to the manual discretization interface of the data import/association. It representsthe current node's data distribution function. The X-axis represents the number of individuals and theY-axis represents the values of the continuous variable.

The user can switch the view of the data to a representation of the density curve generated by theBatch-Means method. In this view, the data's density curve is displayed.The continuous variable's valuesare represented along X-axis and the density of probability is represented along the Y-axis. The two redareas at each extremity indicate that the curve may not be accurate and can't be used to place heresome discretization points.

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This window is fully interactive and allows, in both view:

• Adding a threshold: Right Click

• Removing a threshold: Right Click on the threshold

• Selecting a threshold: Left Click on a threshold

• Moving a threshold: Left Click down and mouse move, the current Y-Coordinate appears in the Pointbox :

• Zooming: Ctrl + Left Click down + move + release to define the area that we want to enlarge. In thedistribution function, the zoom will be done vertically and in the density curve, it will be done horizontally.It is possible to zoom successively as much as you need.

• Unzooming: Ctrl + Double Left Click

Besides this distribution function, the button: allows having access to the threeautomatic discretization methods through a new dialog. This part can be considered a wizard for themanual discretization as it is possible to launch these methods, to see the resulting discretization on thedistribution function, and then to modify the result by moving, deleting and adding thresholds.

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If the chosen discretization fails, a dialog box is displayed to warn the user. In this dialog it can changethe chosen discretization.

When an interval is modified, deleted or added, whatever the way to do this, if data are associated tothe node, then the modified interval values are automatically updated from the data. In the same way,the modified interval names are automatically generated if they are numerical.

If the new manual or automatic discretization is validated by clicking the button Accept of the editor, thedatabase will be automatically updated in order to take into account this new discretization. It will bealso stored as a manual discretization in the database.

3.3.3. Conditional Probability Table

Whereas the arcs connecting the nodes constitute the qualitative part of the network by indicating thedirect probabilistic dependences, conditional probability distributions represent the quantitative part (typeand strength of the probabilistic relations).The most commonly used representation models to describethese distributions are the conditional probability tables.

The reading of a conditional probability table in BayesiaLab is carried out in the following way:

• zone 1 corresponds to the value combinations of the parents of the node. Of course, this zone existsonly if the node has at least one entering arc. When a node has parents, it is possible to change theorder of the parents by dragging the name of the parents inside the header of the zone 1. When aparent is moved, the conditional probability table is reorganized to take the modification into account.

• zone 2 corresponds to the probability distributions, conditionally to each case described by zone 1,or to the a priori probability distribution in the absence of entering arc. If the network has a databaseand the states of the node are not modified, a tool tip displays, for each probabilities, the number of

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corresponding cases in the database (taking into account the smoothing factor, if any) and the rep-resented percentage of the database.

The interpretation of the first line of this table is thus:

• the probability of having Dyspnea is 10% when TbOrCa is False and Bronchitis is False

Table edition

The main problem with conditional probability tables is the exponential growth of the number of lineswith respect to the number of parents. Their data acquisition can then quickly become a tedious task.When databases exist, it is possible to fill them automatically (learning of the parameters). It is alsopossible to use equations to describe more concisely the probability distributions.

The probability acquisition can also be alleviated by using the cut & paste facilities, inside the sametable, between different tables or with external applications.

These tables also come with the classical cell selection tools, either by directly clicking on the cells, orby clicking on the line/column headers. Whereas a click on a header with the key pressed allowsmaking an OR with the previous selection, the same click with the key makes an AND. A click withthe key on a cell allows selecting/unselecting the cell without changing the set of selected cells.This is then the way to edit a cell that belongs to a selection and to set this edit to all the other selectedcells. A click on a cell with the key pressed selects form the active cell to the pointed cell.

Probabilities can be copied and pasted to other tables or to external applications.

Complete

This operation consists in equally distributing the residual probability, defined as being equal to 100 -the sum of the probabilities already defined on the line. If there are blank cells, this residual probabilityis distributed on these cells. Otherwise, if the residual probability is positive, this operation works as theNormalization one over all the cells of the line.

Normalize

Depending on probability probabilities are reduced or augmented in such way that relative weight ofeach remains unchanged there at least a blank cell and if residual is positive this operation correspondsto the complete one.

Randomize

All the cells of the Conditional Probability Table, or just the selected cells, are randomly filled.

Assessment

When experts are associated with the network, a button Assessment is displayed and is activatedwhen a cell is selected. The border of the cells with assessments becomes green and the icon dis-played in the cell indicates how important is the disagreement between the experts for this cell.

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3.3.4. Deterministic nodes

Deterministic nodes are nodes whose relation with their parents is not probabilistic but logical. Whereasthis type of relation can be described by the traditional probability table (with 0 and 100% only), the de-terministic mode allows a faster and more explicit data entry.

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Table edition

Each cell has an associated value list (the node values). This list appears thanks to a double left clickin the cell.

It is possible to select a set of cells by using the line or the column headers, or directly by clicking onthe cells while maintaining the Shift or Ctrl keys pressed, as proposed in the conditional probabilitytables. When several cells are selected, the choice of the value is done by double-clicking on a cellwhile maintaining the Ctrl key pressed. The value that is chosen is then set for all the selected cells.

3.3.5. Equations

The conditional probability tables can be described efficiently by using equations. These equations areapplied for each cell of the probability tables. The results are automatically normalized if necessary. Theedition of equations is realized by using the following node edition panel.

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The equation edition panel is made of 7 parts:

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1. The equation type: allows specifying if the equation returns node values (deterministic) or numericalvalues that will be considered, after normalization, as probabilities (probabilistic). The heading of theequation edition windows (part 2) reflects the choice. Note that the variable appears in the probabil-istic equation to indicate the corresponding column in the probability table.

2. Equation edition window: text field that allows entering equations. The description language of theequations is strongly typed. The syntax used functions and infixed operators.

3. Message panel to display the errors of the formula. If a continuous node has a determinist equation,it is possible that some computed values could be outside the domain of the variable. In this case, adialog box proposes to enlarge automatically the limits of the variable in order to contain these values.

4. This part allows specifying the number of random samples used for the generation of the probabilitytables.These samples are used to sample values inside each interval of the discretized continuousvariables that appear in the equation. This part also allows specifying a smoothing parameter thatis used to initialize the occurrence number of each table cell. Setting this parameter to a valuegreater than 0 implies not only the smoothing of the probability distribution but implies also that allthe states have a non zero associated probability. This smoothing parameter is then unavailable fordeterministic equations.

5. List of the probability distributions, functions and operators that are available to write an equation:

a. Discrete probability distributions

b. Continuous probability distributions

c. Special functions

d. Arithmetic functions

e. Transformation functions

f. Trigonometric functions

g. Relational operators

h. Boolean operators

i. Arithmetic operators

j. User functions

A double-click on the name of the distribution, function or operator, inserts it in the equation.

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6. List of the variables that are available for the equation, i.e. the node that is edited and its parents, ifany. If the parameter Time node is defined in the network, it is available for each equation. If thereare some constants defined in the network, the word Constants is displayed and allows accessingthe list of the available constants when it is selected as you can see it in the following image. A doubleclick on the name of the variable inserts it in the equation. As it can be seen in the following screenshot,the variable names are flanked by question marks when they are referenced in the equation.

7. List of the values of the variable that is selected in part 6 or the available constants if the indicator isselected in part 6. A double-click on a value or on a constant inserts it in the equation.

The constants

To use some constants previously defined as in this example, you have just to select the constant in-dicator in the part 6 and to double-click on the needed constant in the part 7 as shown in the followingimage. The conditional probability table will be recomputed according to the current values of the usedconstants.

Type of the variables

Four types are supported in the equations:

1. Boolean: (true, false), (vrai, faux), (yes, no), (oui, non) (depending on the locale). They are case in-sensitive.

2. String: every quoted list of characters, as for example "az)9*{‘d r&".

3. Integer: defined on the interval [-2147483648, 2147483647].

4. Real: defined on the interval [4.9 E-324, 1.7976931348623157 E308].

Integer and Real belong to the more general type Numerical.

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The variable type is dynamically set during the equation evaluation by using the following rules:

• The discrete variables with only two states defined as true and false, yes or no, vrai and faux, or ouiet non (depending on the locale, case and order insensitive) are typed as Boolean. They can alsobe typed as String, depending on the context of use.

• The discrete variables with states made of characters are typed as String.

• The discrete variables with all the states made of integers are typed as Integer. They can also betyped as String depending on the context of use.

• The discrete variables with all the states made of numbers and at least one of them is a real numberare typed as Real. They can also be typed as String depending on the context of use.

• The continuous variables are typed as Real.

Discrete Probability distributions

NoisyOr(s, leak, c1, p1, cn, pn)

Description: This function represents a noisy Or in which the effect of the parents (the causes ci) onthe symptom s can be inhibited. pi represents the probability that the cause i acts on the symptom (theinhibition probability is then 1-pi). It is also possible to define a leak probability for the set of causes thatare not directly modeled.

Number of Parameters: even, and >= 4

Parameter type: boolean, numerical, boolean, numerical, ..., boolean, numerical

Result type: real

Example: The conditional probability table below corresponds to NoisyOr(?N3?, 0.1, ?N1?, 0.8, ?N2?,0.6)

N3 = TrueN3 = FalseN2N1

0.1(1-0.1)FalseFalse

0.64(1-0.1) * (1-0.6)TrueFalse

0.82(1-0.1) * (1-0.8)FalseTrue

0.928(1-0.1) * (1-0.8) * (1-0.6)

TrueTrue

NoisyAnd(s, leak, c1, p1, cn, pn)

Description: This function represents a noisy And, i.e. the Noisy Or negation.

Number of Parameters: even, and >= 4

Parameter type: boolean, numerical, boolean, numerical, ..., boolean, numerical

Result type: real

Example:The conditional probability table below corresponds to NoisyAnd(?N3?, 0.1, ?N1?, 0.8, ?N2?,0.6)

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N3 = TrueN3 = FalseN2N1

(1-0.1) * (1-0.6) * (1-0.8)

0.928FalseFalse

(1-0.1) * (1-0.8)0.82TrueFalse

(1-0.1) * (1-0.6)0.64FalseTrue

(1-0.1)0.1TrueTrue

Binomial(k, n, p)

Description: Probability of ending up with exactly K occurrences of the same event of probability pamong n independent experiments.

Number of Parameters: 3

Parameter type: integer, integer, numerical

Result type: real

Example: The probability distribution below corresponds to Binomial(?N1?, 20, 0.3)

NegBinomial(k, n, p)

Description: Probability of needing K trials to have n successes of the same event of probability pamong independent experiments.



Result type: real

Example: The probability distribution below corresponds to NegBinomial(?N1?, 4, 0.3)

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Geometric(k, p)

Description: Probability of needing k independent experiments to have the first observation of an eventof probability p.


Parameter type: integer, numerical

Result type: real

Example: The probability distribution below corresponds to Geometric(?N1?, 0.3)

Hypergeometric(k, n, m, N)

Description: Probability of ending up with k winning objects when choosing n objects among N wherem are winning objects.


Parameter type: integer, integer, integer, integer

Result type: real

Example: The probability distribution below corresponds to Hypergeometric(?N1?, 5, 5, 20)

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Poisson(k, l)

Description: Probability of ending up with k observations of an event during a great number of independ-ent experiments when the mean is l.


Parameter type: integer, real

Result type: real

Example: The probability distribution below corresponds to Poisson(?N1?, 18.5)

DiscUniform(k, a, b)

Description: Uniform distribution defined on the discrete interval [a, b].


Parameter type: integer, integer, integer

Result type: real

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Continuous probability distributions

Normal(x, m, s)

Description: Normal distribution of x with mean m and standard deviation s.


Parameter type: numerical, numerical, numerical

Result type: real

Example: The probability distribution below corresponds to Normal(?N1?, 0.3, 0.1)

Triangular(x, m, l, r)

Description:Triangular probability distribution of x with modal value m, left deviation l and right deviationr.


Parameter type: numerical, numerical, numerical, numerical

Result type: real

Example: The probability distribution below corresponds to Triangular(?N1?, 0.5, 0.2, 0.4)

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Cauchy(x, m, s)

Description: Cauchy probability distribution of x with modal value m and scale s.



Result type: real

Example: The probability distribution below corresponds to Cauchy(?N1?, 0.5, 0.1)

Exponential(x, l)

Description: Exponential probability distribution of x with lambda = l.


Parameter type: numerical, numerical

Result type: real

Example: The probability distribution below corresponds to Exponential(?N1?, 2)

Weibull(x, a, l)

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Description: Weibull probability distribution of x. Note that Weibull(x, 1, l) = Exponential(x, l).



Result type: real

Example: The probability distribution below corresponds to Weibull(?N1?, 1.5, 1.5)

Gamma(x, a, l)

Description: Gamma probability distribution of x. Gamma(x, 1, l) = Exponential(x, l).



Result type: real

Example: The probability distribution below corresponds to Gamma(?N1?, 1.5, 1.5)

Beta(x, a, b, bi, bs)

Description: Beta probability distribution of x.

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Number of Parameters: 5, the last two ones represent the lower and upper bounds of the variable withdefault values 0 and 1 respectively.

Parameter type: numerical, numerical, numerical, numerical, numerical

Result type: real

Example: The probability distribution below corresponds to Beta(?N1?, 2, 5, 0, 5)

ChiSquare(x, n)

Description: Chi-Square probability distribution of x with n degrees of freedom.


Parameter type: numerical, integer

Result type: real

Example: The probability distribution below corresponds to ChiSquare(?N1?, 3)

LogNormal(x, m, s)

Description: Log normal probability distribution of x.


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Result type: real

Example: The probability distribution below corresponds to LogNormal(?N1?, 0.4, 0.8)

Uniform(x, a, b)

Description: Uniform probability distribution of x on the interval [a, b].



Result type: real

Special functions

If(c,t,e)

Description: Conditional instruction: Ifc is True thentelsee.

Number ofParameters: 3

Parameter type: boolean, all, all, but the last two parameters have to be of the same type or comparable(integer and real).

Result type: The type of the result is the type of the last two parameters. If one of them is real and theother integer, then the result type is real.

Example: The following probability distributions correspond to:

P(?Opinion? | ?Note?) =

If(?Opinion? == "Very weak", Normal(?Note?, 0, 3.5),

If(?Opinion? == "Weak", Normal(?Note?, 7, 3),

If(?Opinion? == "Fair", Normal(?Note?, 10, 3),

If(?Opinion? == "Good", Normal(?Note?, 13, 3), Normal(?Note?, 20, 3.5)))))

where Opinion is a Discrete variable that has 5 states (Very weak, Weak, Fair, Good, Very good) andNote is a Discrete variable with 21 integer states from 0 to 20.

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Switch(s, ki, vi, ..., d)

Description: Branch instruction. According to the value ki that s can take, the corresponding value viis returned. If no ki is corresponding, then the default value d is returned.

Number of Parameters: >= 4

Parametertype: all, all, all, ..., all but the parameters s and ki must have the same type or comparable(integer and real for example) and it must be the same thing for the parameters vi and d.

Result type: The return type is the common type of the parameters vi and d. If one of them is real andthe other integer, then the result type is real.

Example: The previous probability distributions correspond to:

P(?Opinion? | ?Note?) =

Switch(?Opinion?,

"Very Weak", Normal(?Note?, 0, 3.5),

"Weak", Normal(?Note?, 7, 3),

"Fair", Normal(?Note?, 10, 3),

"Good", Normal(?Note?, 13, 3),

Normal(?Note?, 20, 3.5))

where Opinion is a Discrete variable that has 5 states (Very weak, Weak, Fair, Good, Very good) andNote is a Discrete variable with 21 integer states from 0 to 20.

CumulBinomial(k, n, p)

Description: Normalized cumulated probability of ending up with K or less occurrences of the sameevent of probability p among n independent experiments.


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Result type: real

RandomUniform(min, max)

Description: Returns a real value greater than or equal to min and less than max. Returned values arechosen pseudo randomly with (approximately) uniform distribution from that range.


Parametertype: numerical, numerical

Result type: real

RandomGaussian(m, s)

Description: Returns the next pseudo random, Gaussian ("normally") distributed real value with meanm and standard deviation s from this random number generator's sequence.

Number ofParameters: 2


Result type: real

Arithmetic functions

Abs(x)

Description: Absolute value of x.

Number of Parameter: 1

Parametertype: numerical

Result type: numerical

Ceil(x)

Description: Nearest integer greater than or equal to x.



Result type: real

Exp(x)

Description: Exponential of x.



Result type: real

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Fact(n)

Description: Factorial of n.


Parametertype: integer >= 0

Result type: integer

Floor(x)

Description: Nearest integer less than or equal to x.



Result type: real

Frac(x)

Description: Fractional part of x.



Result type: real

Integer(x)

Description: Integer corresponding to x. When x is positive, it's Floor(x) and it's Ceil(x) otherwise.



Result type: real

Ln(x)

Description: Natural logarithm of x.



Result type: real

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Log(x)

Description: Common logarithm of x.



Result type: real

Log2(x)

Description: Binary (base 2) logarithm of x.



Result type: real

Max(x1, x2)

Description: Maximum between x1 and x2.




Min(x1, x2)

Description: Minimum between x1 and x2.




Sqrt(x)

Description: Square root of x.



Result type: real

Transformation functions

Clip(x,min,max)

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Description: Clip x to the interval [min, max].


Parametertype: numerical, numerical, numerical

Result type: real

Round(x)

Description: Nearest integer less than or equal to x if the fractional part is less than 1/2, nearest integergreater than or equal to x otherwise.



Result type: real

RoundTo(x, n)

Description: Round of x to n digit after (if n is negative) or before the decimal point (if n is positive).When n is equal to 0, this function is identical to Round(x).


Parametertype: numerical, integer

Result type: real

Sign(x)

Description: Returns -1, 0 or 1 depending on the sign of x.




Trigonometric functions

Sin(x)

Description: Sine of x.



Result type: real

Cos(x)

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Description: Cosine of x.



Result type: real

Tan(x)

Description: Tangent of x.



Result type: real

Asin(x)

Description: Inverse sine of x.



Result type: real

Acos(x)

Description: Inverse cosine of x.



Result type: real

Atan(x)

Description: Inverse tangent of x.



Result type: real

Sinh(x)

Description: Hyperbolic sine of x.

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Result type: real

Cosh(x)

Description: Hyperbolic cosine of x.



Result type: real

Tanh(x)

Description: Hyperbolic tangent of x.



Result type: real

Relational operators

The priority of the operators is defined from 1 to 9, 9 being the strongest priority.

<, <=, >, >=

Description: Comparison operators.



Result type: boolean

Priority: 5

==, !=

Description: Equality and non equality operators.


Parametertype: the two parameters have to be of the same type or numerical


Priority: 4

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Boolean operators


!

Description: Negation operator.

Parameter number: 1

Parametertype: boolean


Priority: 8

XOR

Description: Exclusive Or operator.

Parameter number: 2

Parametertype: boolean, boolean


Priority: 3

&

Description: And operator.

Parameter number: 2



Priority: 2

|

Description: Or operator.

Parameter number: 2



Priority: 1

Arithmetic operators


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^

Description: Exponentiation operator.


Parametertype: numerical, integer


Priority: 9

-

Description: Negation operator.




Priority: 8

%

Description: Modulo operator.


Parametertype: integer, integer


Priority: 7

*

Description: Multiplication operator.




Priority: 7

/

Description: Division operator.


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Result type: real

Priority: 7

+, -

Description: Addition and subtraction operators.




Priority: 6

Plugins for the equations

Description

BayesiaLab can include automatically functions defined by the user in its equation editor, in order to usethem to generate the conditional probability tables of the nodes. The defined functions can have a vari-able number of parameters. It is possible to interface Java, C, C++, FORTRAN, Mathematica, etc. Thiscan be done directly, through JNI or some specialized libraries. For all information and advice you cancontact Bayesia S.A.

Architecture

To allow this integration, a Java interface is included in the library BayesiaLab.jar located in theBayesiaLab's installation directory. In order to create its own function, the user must 'implement' thisinterface with its own Java class. Once its class created, a jar library file must be created and copiedinto a directory named "ext" which is a sub-directory of the BayesiaLab's running directory. If the createdJava library needs some additional files, they must be located in the running directory of BayesiaLabor in its sub-directory "ext". In this last case, you must remember to specify in your program to look forthe additional files in the ext sub-directory.

For Windows, the path is: C:\Documents and Settings\All Users\Application Data\BayesiaLab\ext

Interface

The Java interface that must be implemented is called ExternalFunction and is located in the packagecom.Bayesia.BayesiaLab.ext

Here is its content:

package com.Bayesia.BayesiaLab.ext;

public interface ExternalFunction {

/*** Define the real type.*/public static final int REAL = 1;/**

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* Define the integer type.*/public static final int INTEGER = 2;/*** Define the boolean type.*/public static final int BOOLEAN = 3;/*** Define the String type.*/public static final int STRING = 4;/*** This method is called once when the object is created, i.e.* when the formula is built.* It can be used to create structures that will be constant * for all the life time of the formula it is part of.* @return true if the initialization process succeed otherwise false*/public boolean initialization();/*** This method is called once, when the object is no more used * and the object will be destroyed.* @return true if the initialization process succeed otherwise false*/public boolean finalization();/*** This method is called before the generation of the conditional * probability tables.* It indicates how many calls to the method evaluate() will be done.* For example a binary node with* two binary parents will need 2*2*2=8 combinations, and if this * node or any of its parent is continuous,* the number of sample that will be generated for each combination* (1000 for example) will be given as sample number.* @param combinationNumber the number of combinations the * conditional probability table represents.* @param sampleNumber the number of samples that will be executed * if at least one node is continuous.*/public void beforeEvaluation(int combinationNumber, int sampleNumber);/*** This method is called after the evaluation of * all the combinations.*/public void afterEvaluation();/*** This is the main method the evaluates the function for each * given combination of parameters.* If an error has occurred during the evaluation, an * ArithmeticException must be thrown with the convenient * error message.* @throws ArithmeticException if an error has occurred during the* evaluation*/public void evaluate() throws ArithmeticException;/*** Return the name of the function that will be displayed * in BayesiaLab and recognized by the formula parser.

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* @return a String representing the name of the function*/public String getName();/*** Return the description of the function that will be displayed * in as a tooltip in BayesiaLab. This string can contains html tags.* @return a String describing the function*/public String getDescription();/*** This method indicates if the number of parameters is variable.* If true, the method getParameterNumber() indicates the minimum* number of parameters that the function accepts.* @return true if the parameter number is variable false otherwise* @see #getParameterNumber()*/public boolean isVariableParameterNumber();/*** This method is used to indicate to the function what is the number of parameters * that will be used when the parameter number is variable.* This method is called after the creation of the instance.* parameterNumber must be superior or equal to the * value returned by getParameterNumber().* @see #getParameterNumber()* @see #isVariableParameterNumber()*/public void setUsedParameterNumber(int parameterNumber);/*** Return the number of parameters the function uses.* If the number of parameters is variable, it indicates the minimum number* of parameters used by the function.* @return the number of parameters* @see #isVariableParameterNumber()*/public int getParameterNumber();/*** Return the name of the parameter at the specified index * (from 0 to n). If the parameter number is variable, this method * will be called only for the first parameters until * getParameterNumber().* @param parameterIndex the index of the parameter* @return the name of the parameter* @see #getParameterNumber()* @see #isVariableParameterNumber()*/public String getParameterNameAt(int parameterIndex);/*** Return the type of the parameter at the specified index * (from 0 to n).* The type must be one of REAL, INTEGER, BOOLEAN or STRING.* @param parameterIndex the index of the parameter* @return the type of the parameter*/public int getParameterTypeAt(int parameterIndex);/*** Return the type of the value returned by the function.* The type must be one of REAL, INTEGER, BOOLEAN or STRING.* @return the type of the returned value

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*/public int getReturnType();/*** Sets the integer value of the parameter at parameterIndex.* The type of the parameter must be one of INTEGER or REAL.* @param parameterIndex the index of the parameter* @param value the integer value associated to the parameter*/public void setParameterValueAt(int parameterIndex, int value);/*** Sets the double value of the parameter at parameterIndex.* The type of the parameter must be REAL.* @param parameterIndex the index of the parameter* @param value the double value associated to the parameter*/public void setParameterValueAt(int parameterIndex, double value);/*** Sets the boolean value of the parameter at parameterIndex.* The type of the parameter must be BOOLEAN.* @param parameterIndex the index of the parameter* @param value the boolean value associated to the parameter*/public void setParameterValueAt(int parameterIndex, boolean value);/*** Sets the string value of the parameter at parameterIndex.* The type of the parameter must be STRING.* @param parameterIndex the index of the parameter* @param value the String value associated to the parameter*/public void setParameterValueAt(int parameterIndex, String value);/*** This method is called to get the result of the evaluation if* the return type is INTEGER.* @return the result of the evaluation as integer*/public int getIntegerResult();/*** This method is called to get the result of the evaluation if* the return type is REAL.* @return the result of the evaluation as double*/public double getRealResult();/*** This method is called to get the result of the evaluation if* the return type is BOOLEAN.* @return the result of the evaluation as boolean*/public boolean getBooleanResult();/*** This method is called to get the result of the evaluation if* the return type is STRING.* @return the result of the evaluation as String*/public String getStringResult();

}

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Example of implementation

The following example use a Windows dynamic library (dll) that returns the sum of two real numbers.

import com.Bayesia.BayesiaLab.ext.*;

public class Sum implements ExternalFunction {

/*** Allows to load the library that performs the * computation and located in the ext sub-directory * of the execution directory of BayesiaLab.*/static { System.loadLibrary("ext/Sum");}/*** An array defining the name of the parameters.*/private static final String[] parameters = {"a", "b"};/*** An array defining the type of the parameters.*/private static final int[] parameterTypes = {REAL, REAL};/*** An array to store the values of the parameters.*/private double[] values = new double[2];/*** Represents the result of the computation.* It is initialized with Not a Number.*/private double result = Double.NaN;/*** This method is linked to the method defined in * the library Sum that performs the computations.* @param a* @param b* @return the sum of a and b*/private native double compute(double a, double b);/*** The method calls the method compute with the parameters*/public void evaluate() throws ArithmeticException { result = compute(values[0], values[1]);}/*** Nothing to do.*/public boolean initialization() {return true;}/*** Nothing to do.*/

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public boolean finalization() {return true;}/*** Nothing to do.*/public void beforeEvaluation(int combinationNumber, int sampleNumber) {}/*** Nothing to do.*/public void afterEvaluation() {}/*** The name of the function is Sum.*/public String getName() { return "Sum";}public String getDescription() { return "Return the sum of the real numbers a and b.";}public boolean isVariableParameterNumber() { return false;}/*** Nothing to do because there is variable parameter number.*/public void setUsedParameterNumber(int parameterNumber) {}public int getParameterNumber() { return parameters.length;}public String getParameterNameAt(int parameterIndex) { return parameters[parameterIndex];}public int getParameterTypeAt(int parameterIndex) { return parameterTypes[parameterIndex];}public int getReturnType() { return REAL;}/*** Nothing to do because there is no integer parameter.*/public void setParameterValueAt(int parameterIndex, int value) {}/*** Give the real value to the parameter at the specified index.*/public void setParameterValueAt(int parameterIndex, double value) { values[parameterIndex] = value;}/*** Nothing to do because there is no boolean parameter.*/public void setParameterValueAt(int parameterIndex, boolean value) {}

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/*** Nothing to do because there is no String parameter.*/public void setParameterValueAt(int parameterIndex, String value) {}/*** Return 0 by default. It won't be called.*/public int getIntegerResult() { return 0;}/*** Return the result of the computation.*/public double getRealResult() { return result;}/*** Return false by default. It won't be called.*/public boolean getBooleanResult() { return false;}/*** Return null by default. It won't be called.*/public String getStringResult() { return null;}

}

Compilation

The command line used to compile the java class is :

javac -cp "C:\Program Files\Bayesia\BayesiaLab\BayesiaLab.jar" Sum.java

It may be necessary to indicate the path to the javac.exe program located in the bin directory of thejdk1.6.

The Sum.class file will be generated.

Generating the header file for the C++ library

In order that java can call the corresponding function in C++, it is necessary to generate a C++ headerfile to include it in the library (dll for Windows). The command line used to generate the .h file is:

javah Sum

It may be necessary to indicate the path to the javah.exe program located in the bin directory of thejdk1.6.

The Sum.h file will be generated.

/* DO NOT EDIT THIS FILE - it is machine generated */#include <jni.h>

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/* Header for class Sum */

#ifndef _Included_Sum#define _Included_Sum#ifdef __cplusplusextern "C" {#endif/** Class: Sum* Method: compute* Signature: (DD)D*/JNIEXPORT jdouble JNICALL Java_Sum_compute(JNIEnv *, jobject, jdouble, jdouble);

#ifdef __cplusplus}#endif#endif

This file must not be modified. For more information on JNI (Java Native Interface) consult Internet.

Jar file generation

Once the Sum.java file compiled into Sum.class, you have to create the jar library file. Simply run thefollowing command line :

jar -cf Sum.jar Sum.class

The Sum.jar file is generated and must be put in the ext sub-directory of the BayesiaLab's runningdirectory.

The Sum.dll library must be put in the ext sub-directory of the BayesiaLab's running directory.

Starting

After having created its plugin and after the restart of BayesiaLab, the plugin is loaded and is availablein the equation editor:

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3.3.6. Assessments

The mechanism of knowledge elicitation of BayesiaLab allows a set of experts to provide assessmentson the conditional probability tables of nodes. A "facilitator" can mediate to ask relevant questions toexperts and get their assessments.

The experts must be declared in the network with the expert editor.

Two ways of capturing the assessments are proposed:

• Each assessment is input directly in BayesiaLab.

• Or each assessment is input via the online assessment tool.

When a node has assessments, the icon is displayed at the bottom left of the node. More the dis-agreement between the assessments is important for this node, more the background of the icon becomesdark.

A slideshow explains the principle of knowledge elicitation in BayesiaLab. It can be found at the followingaddress:http://www.bayesia.com/en/products/bayesialab/resources/tutorials/bayesiaLab-know-ledge-elicitation-environment.php

Assessments can be entered from the tab Probability Distribution in the node editor. Experts musthave been already created. In this case, a button Assessment is displayed and becomes activablewhen a cell is selected. After pressing the button, the assessment edition is done for the selected line.

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When an assessment was made for a line in the conditional probability table, the corresponding cellshave a green border.The icon displayed in the cell indicates the importance of disagreement betweenthe experts for this cell. More the icon is visible, more the disagreement is important.

Move your mouse over a cell displays a tooltip showing:

• The minimum given by an expert for this cell

• The maximum given by an expert for this cell

• The number of assessments for this cell

Editor

The assessment editor displays the list of assessments for the selected line of the conditional probabilitytable.

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A line in this table defines an assessment. This assessment consists of:

• A probability for each state of the node, the sum of probabilities to be equal to 100. The backgroundof the corresponding cells is gray. These values can be edited by double-clicking or by typing thevalue if the cell is selected.

• The name of the expert who has made this assessment. The expert is chosen from a combo boxcontaining the name of each expert.

• The confidence the expert gives to his assessment. This value is editable.

• The comment the expert makes about his assessment. A tooltip containing the entire comment isdisplayed when we move the mouse over the cell.

• The time taken to make this expertise. It is measured in seconds.This value is editable. It is 0 by defaultwhen the expertise is filled manually. However, it is automatically filled in when the expertise is online.

The button Add adds an assessment by default at the end of the list.This assessment will then be editedmanually. It is possible to have several assessments from the same expert, but, for clarity, it is not re-commended.

The button Delete deletes the selected assessments.

When an assessment is selected the expert's image is displayed on the right side:

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Assessment Validation

When you press the button Accept of the dialog box, assessments are automatically normalized if ne-cessary, the sum of probabilities to be equal to 100. Then, the consensus is computed. He will serveas a probability distribution in the conditional probability table of the node for the corresponding row.This consensus is computed by averaging assessments for each state weighted by the confidence ofeach expert. The assessment whose confidence is equal to zero will not be taken into account.

Online Editing

When an online knowledged elicitation session has been created, a button Post Assessment isdisplayed in the window.

When you press this button, the current question is posted online so that experts can answer it connectedvia a dedicated web interface. This question asks the experts to get the probability distribution that cor-responds to the chosen line of the conditional probability table. If assessments already exist for thisquestion, the web interface for relevant experts will be pre-filled.A window displays, in real-time, theexperts who anwsered the question:

This table can be sorted by clicking on the header of each column.

Web Interface

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Once the online session has been opened, an expert can connect with its Internet browser to followingsecured address:https://www.bayesialab.com

He will enter his expert name and the name of the session respecting upper case:

Once connected, the waiting interface will be displayed:

Once a question is posted through BayesiaLab, it will appear in the interface of each expert. If the experthas already answered this question, the corresponding fields are already filled. They may be modifiedif necessary.

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On the right side, the name and the comment of the node are displayed. A colored slider and a fieldallows editing the probability associated with each state the node. When the probability of a state ischanged, the others will be adjusted in order to always sum to 100. A lock located on the left allowsblocking the corresponding probability so it is no longer editable. The probability can be unlocked byclicking again on the lock.

The expert can also enter the confidence it grants to its assessment.

A text field lets you enter the comment associated with this assessment.

On the left, the context of the question is displayed, i.e. the current states of each parent of the node.By hovering the name of the parents, their comments will be displayed in a tooltip.

The pie chart in the bottom left reproduces the current probability distribution. A textual indicator indic-ates in a simplified way the confidence of the assessment.

The button Validation sends the anwser of the expert to the server then the indicator of experts whohave answered is updated on BayesiaLab. After that, the waiting interface is displayed again.

Tools

The contextual menu of the expert indicator allows us to generate an assessment report.

The menu Tools > Assessment provides access to various tools for exporting assessments.

The menu Analysis > Graphic provides access to the assessment sensitivity analysis.

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3.4. Node States

The fundamental element of the graphical representation is the node. The nodes in BayesiaLab havetwo possible types, each one with its own graphical representation :

• Discrete, for the variables with discrete values:

• Continuous, for the variables that have numerical continuous values:

Furthermore, a node (Discrete or Continuous) has various possible states, each one being representedby a different visualization:

• Normal: the node in the standard state (node N1);

• Selected: the selection makes it possible to carry out operations like Move, Delete, Monitor, etc. (nodeN2);

• Monitored: a monitored node has an associated monitor in the monitoring panel (node N3);

• Hard evidence: an observed node (node N4) represents a random variable that has been observed.Based on these observations, it is possible to start a probabilistic inference to compute the probab-ilities of the unobserved random variables knowing the value of the observed ones;

• Soft evidence: a soft observed node (node N5) represents a random variable for which the user hasentered likelihoods.

• Simple probability: a node with simple probability set (node N5) represents a random variable forwhich the user has entered likelihoods from probabilities.

• Fixed probability: a node with fixed probability (node N9) represents a random variable for whichthe user has entered fixed probabilities.

• Target: a target node (node N6) is a particular node (possibly having a target value) that specifiesfocusing the analysis algorithms on that node (in validation mode), or to direct the learning process(supervised learning)

• Machine learning: the design of the structure is fully focused on the characterization of this node;

• Evaluation: the precision of the prediction of the Bayesian network is measured with respect tothe target node. The target value is used for measuring the precision with the Gain, Lift and ROCcurves.

• Analysis: the analysis is carried out to measure the influence of the network variables on theknowledge of the target variable (Target Node Analysis, Target Analysis Report), or on theknowledge of the target state (Target State Analysis: accurate analysis of the influence of a variableon the target state). The target node is also used to specify the root evidence that is necessary togenerate the Evidence Analysis Report.

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• Inference: the value of the target is inferred for each case described in a database (Batch Exploit-ation);

• Decision-making aid: development of an adaptive questionnaire focused on the knowledge of thetarget variable, or focused on the knowledge of the target state.

• Temporally spied: a node can be temporally spied only if it belongs to a dynamic Bayesian network.This node state indicates that the probability evolution of a particular value of this node (node N7) willbe followed in a chart and possibly in an output file during the temporal simulation.

• Hidden: this kind of nodes (node N8) corresponds to the nodes that are created while there is adatabase associated to the network. These nodes do not have any corresponding data in the base(typically, the Cluster node is a hidden node). These nodes can be used to create new conceptsbased on nodes that exist in the base. As in Clustering, it is possible to connect hidden nodes to asubset of nodes, to indicate the number of states, and to learn the parameters. Once the learningparameters is achieved, Taboo learning (the only Association Discovery algorithm that does notremove the existing arcs when launching) can be used to integrate these hidden nodes to the rest ofthe networks.

• Not observable: this kind of nodes (node N9) corresponds to the nodes that have no associatedcost.

• Translucent: a node (node N10) can become translucent for various reasons. In this case, it is notselectable anymore. The possible causes are:

• it doesn't belong to a displayed class

• its arcs are filtered by the Pearson's correlation

• the current mode is the neighborhood analysis

• etc.If the comment associated to the node is shown on screen, it becomes translucent as well.

• Excluded: this kind of node (node N11) corresponds to the nodes which must not be taken into accountduring learning. It is possible to exclude a node or to include it thanks to the contextual menu of thenode. When a node is excluded, the supervised or structural learning algorithms do not add anyrelationships of which one of the ends is this node. The MDL score is modified accordingly.

Beyond these states, the nodes can be tagged by a Warning or an Error . In the last case, itmeans that there is an error the formula of the node (after changing the parent nodes). The warning in-dicates either that the formula is not verified, or that the conditional probability table is not edited, or thatthe probabilities do not sum to 100. Keeping pressed while pointing on one of those icons allowsdisplaying the corresponding error/warning message.

The icon , displayed at the bottom left of the node, indicates if assessments are associated with thisnode. More the disagreement between the assessments is important for this node, more the backgroundof the icon becomes dark. Pressing while hovering on the icon displays the following information:

• the number of conditional probability table's rows with assessments compared to the total number ofrows

• the total number of assessments

• the number of experts involved compared to the total number of expert

• the global disagreement

• the maximum disagreement

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The icon , displayed at the top right of the node, indicates if there is missing values in the databaseassociated to the network. Pressing while hovering on the icon displays the number of missing valuesassociated to this node.

The icon , displayed at the bottom right of the node, indicates if one of the node's states is defined asa filtered state.

The icon , displayed at the right of the node's name indicates if there is a comment associated to thenode. Pressing while hovering on the icon displays the comment associated to this node.

All these indicators can be hidden with the button or menu hide information in the View menu or inthe display toolbar.

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3.5. Constraint node

A constraint node is a node used to express constraint relations that have to hold between nodes(e.g. two nodes cannot have the same value).

• It is a logical node (with only two values: True and False),

• it is always observed to the True value ,

• it is impossible to monitor it, to add or rename states.

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3.6. Utility node

A utility node is a node that allows valuating the states defined by the state combinations of its parents.

In the following example, the utility node U1 valuates the states defined by Playing inside or outsidewhen the weather is dry or wet. Following the utility table below, the best case corresponds to play outsidewith a dry weather, the worst one being playing outside when it rains. It is also possible to describe theseutilities with equations.

The arcs that link chance nodes and utility nodes are fixed to prevent arc inversion. Indeed, utility nodescannot have outing arcs.

In Validation Mode, the expected value of a utility node is displayed in a specific monitor.

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3.7. Decision node

A decision node is a node that allows representing actions, and then that makes it possible to describepolicies.

The parents of a Decision node define its perception, i.e. the optimal action can vary with respect to thevalues of the parents.

The probabilistic effects of actions are modeled thanks to the classical conditional probability tables thatare associated with the children of the Decision nodes.

The conditional probability table of a decision node is replaced by a quality table that indicates, for eachperceived state, i.e. each parent state combinations, the quality of actions.These qualities can be definedby the user (directly or by using equations) and/or automatically learned by the BayesiaLab's learningalgorithms.

As it can be seen in the screen shot above, the best policy (the best action for each state) is describedwith blue background cells in the quality table of the Decision node.

In Validation Mode, the best action is displayed in a specific monitor, and its expected value can bedisplayed by pressing while pointing on the monitor.

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3.8. Arc Management

An arc is created either in the creation mode (see Use) or by using the shortcut + click. When a loopis introduced by adding an arc, the following dialog box is displayed :

The button Display loops displays the following dialog box showing the different introduced loops andtheir length. Selecting a loop in the list displays the arcs that belong to the loop in pink in the graph.

Arc inversion

An arc can be inverted by using the contextual menu that is activated by a left click on the arc (or onan arc belonging to the selection). In modeling mode, any arc can be inverted (but the conditionalprobability tables are lost). In Validation mode, an arc can only be inverted when that inversion leads toan equivalent graph, i.e. a graph belonging to an equivalent class (the conditional probability tablesare then modified so that the probability law remains unchanged).

Fix the arc

An arc can be fixed by the mean of the contextual menu activated by a left click on the arc (or on anarc belonging to the selection).

Creation of a temporal arc

A temporal relation (and then the transformation of the Bayesian network into a dynamic Bayesian net-work) is realized by the mean of the contextual menu that is activated by a left click on the arc (or onan arc belonging to the selection).

Arc deletion

The deletion of an arc is made either in the deletion mode (see Use) or by using the shortcut + click.

Move an arc

A node is moved by keeping pressed during the drag operation. An arc can only be moved if theinitial origin node has the same number of states as the final origin node. The probability table is con-served.

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Edge display

Displaying edges is only allowed in Validation mode. It can be done by using the Inference menu ordirectly by the mean of the shortcut . This function is unavailable for dynamic Bayesian networksand approximate inference.

Edge orientation

It is only possible to set an orientation to an edge in Validation mode. It can be done by using the Infer-ence menu or directly by the mean of the shortcut . Edges are automatically directed when switchingto modeling mode.This function is unavailable for dynamic Bayesian networks and approximate inference.

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3.9. Arc states

An arc (directed from an origin node towards a destination node) represents a direct probabilistic relationbetween the two linked nodes.The creation of an arc implies a new entry in the probability table associatedwith the destination node of this arc.

An arc can be in one of these 4 states:

• normal: the arc in a standard state (arc from N1 towards N3);

• selected: the selection makes it possible to carry out operations like Invert, Delete, etc. (arc from N2towards N3);

• fixed: a fixed arc (arc from N1 towards N2) is a mean to introduce a priori knowledge on the networkstructure before learning;

• temporal: a temporal arc indicates a temporal relation between two particular nodes: the father node(Node t) represents a variable at time step t whereas the child node represents the same variable attime step t+1 (Node t+1). These two nodes must thus be strictly identical. In addition, a node can onlyhave one single temporal child. A temporal arc transforms the network in a dynamic Bayesiannetwork.

An arc can become translucent for various reasons:

• one of its extremities doesn't belong to a displayed class

• it is filtered by the Pearson's correlation

• etc.

In this case, it is not selectable anymore. If the comment associated with the arc is shown on the screen,it becomes translucent also.

In Validation mode, it is also possible to have not oriented arcs (edges) to indicate that the orientationof the arc can be changed without modifying the joint probability law.

The icon , displayed at the middle of the arc name indicates if there is a comment associated to thearc. Pressing while hovering on the icon displays the comment associated to this arc.

Lastly, in Validation mode, the node contextual menu allows highlighting the arcs that belong to theinfluence paths between a node and the target node.Those paths indicate by which way the informationgoes from the node to the target node (and conversely). The screenshot below illustrates this function-ality. Three information paths link Dyspnea and Cancer, the number in brackets corresponds to thelength of the path.

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This analysis, that illustrates the d-separation concept, takes into account the context, i.e. the evidencesthat have been entered, as illustrated below.Without any evidence concerning the Dyspnea value, thereis no information path that links VisitAsia and Cancer. However, knowing the value of that node opensthree influence paths.

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3.10. Filtered States

For each node, discrete or continuous, it is possible to define one and only one filtered state among allthe states of the node. This state allows us to represent the cases where the variable doesn't have areal existence according to the other variables of the network. It is the case when the current variablehas a value only if another variable has a specific value. For example, let us take the case of a vari-able Analysis which is performed only according to the result of a variable Test:

The variable Test has two states: "True", "False".

The variable Analysis has three states: "Positive", "Negative" and "Not applicable" (also noted "*") thatwill be defined as a filtered state

• if the value of the variable Test is "True" then the value of the variable Analysis can be "Positive" or"Negative" according to a certain probability distribution

• if the value of the variable Test is "False" then the value of the variable Analysis will be the filteredvalue "Not applicable" (or "*")

This configuration very often occurs in the results of questionnaires, surveys, etc, where questions oritems are asked or not according to the answer to the preceding question. The problem is thatwhen the structure of a network is learned with this type of data, very strong structural relations betweenthe "pivot" variables (like the variable Test) and the "conditional" variables (like the variable Analysis)are systematically extracted to represent this dependence while bringing, generally, no "interesting" in-formation to the model. The important thing to learn is the behavior of the "conditional" variables withregards to the model only when they exist, i.e. on data sample in which them value is different from thefiltered value. The definition a filtered state allows doing this.

Filtered state indicators

When a network has filtered states, the filtered state indicator is displayed in the network's statusbar.

If a node has a filtered state, the icon will be displayed on the node.

If a node has a filtered state, its monitor will display the icon in front of the corresponding state, aswe can see it in the following picture:

Importing/Associating data containing filtered values

It is possible to define a filtered state at data importation or at data association. In this case all thefiltered values of the database will be replaced by the character *. At the end of importation, for eachnode containing a filtered value, a filtered state will be added to the list of the states present in thedatabase. Concerning continuous nodes, a new interval of width 1E-7 will be added after the intervalsdefined during importation.The name of this interval will be * and it will be considered as a filtered state.

In the case of data association, if the variable is added then the behavior is the same as at importation,if not, if it already exists and it is a continuous variable, several cases are to be differentiated:

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1. No initially filtered state in the continuous node, filtered values in the database: an interval of width1E-7 will be added after the intervals defined in the node.

2. Initially filtered state in the continuous node and no filtered value in the database: the imported valueswhich correspond to the interval of the filtered state are treated as filtered values.

3. Initially filtered state in the continuous node and filtered values in the database: the imported valueswhich correspond to the interval of the filtered state are treated as filtered values and the importedfiltered values are also associated with this interval.

Editing filtered states

The node editor has a specific panel allowing us to manually define one filtered state by node.

Filtered states dictionary

It is possible to define the filtered states of the nodes in the network by using a dictionary. It is alsopossible to export a dictionary containing the filtered states of the network.

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3.11. Class management

The classes allow defining sets of nodes which have common properties. That makes it possible togather variables according to their given sense, for example. The node can belong to several classesat the same time. Once these classes defined, it is possible to apply certain properties to each nodecomposing a class. Through the interface, it is possible to give a color, an image, a temporal index ora cost to the nodes of a class. These classes of nodes can be also used in the edition of the forbiddenarcs: it is possible to forbid arcs between two classes of nodes, a node and a class and a class and anode.

Class editor

The class editor is accessible by the contextual menu associated to the graph. The table shows thelist of the classes with the number of nodes they contain. It is possible to rename a class by double-clicking on its name in the table.

The table is sortable by clicking on the header of each column.

Add a class

The Add button displays the following dialog box in order to enter the name of the class, which must bedifferent from the others:

Once a valid name is entered, you have to select the nodes that you want to add in the class:

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Modify a class

The Modify button displays a dialog box which is the same as the previous one and that allows managingthe content of the class. It is possible to add or remove nodes from this class. If no node remains andyou validate, the class will be deleted.

Delete a class

The Delete button removes all the classes selected in the table.

Apply a color

The Color button displays the following dialog box in order to associate a chosen color to the nodes ofthe selected classes if the first checkbox is selected or to associate a distinct color to each selectedclass if the last checkbox is selected. In this case, a random color will be associated with the nodes ofeach class. If no checkbox is selected, the color of the nodes will be removed.

Apply an image

The Image button displays the following dialog box in order to associate a chosen image to the nodesof the selected classes. If the checkbox is not selected, the images of the nodes will be removed.

Apply a temporal index

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The Temporal index button displays the following dialog box in order to associate a temporal index tothe nodes of the selected classes. If the checkbox is not selected, the temporal indices of the nodes willbe removed.

Apply a cost

The Cost button displays the following dialog box in order to associate a cost to the nodes of the selectedclasses. If the checkbox is not selected, the nodes will be not observable.

Note

It is not the classes to which these properties are applied but to the nodes contained in these classesat the time when these properties are applied. If a node is added to a class after having applied aproperty, this node will not have this property.

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3.12. Constant management

A constant allows keeping a global value in the Bayesian network in order to be used in the equationsrepresenting the probability distributions of the variables. The constants can be created and to havetheir value modified only in modeling mode. When we switch into validation mode, the conditionalprobability tables of the variables which use constants in their equation are recomputed according tothe new values of the constants. In the equations, the constants are handled by their name, like thevariables.

A variable is defined by a name which must be unique in the Bayesian network, a type which can beBoolean, integer, real or character string. Once the constant created, its value can be modified at will.

Constant editor

The constant editor is accessible by the contextual menu associated with the graph.This table displaysthe list of the constants. For each constant, its name, its type and its current value are displayed. Thevalues are editable by double-clicking on the corresponding cell.


Add a constant

The Add button displays the following dialog box allowing entering the name of the constant, which mustbe unique in the network, the type of the constant and its value:

Delete a constant

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The Remove button deletes all the selected constants. After validating, the nodes having their equationthat uses a deleted constant are displayed with the icon: .

Modify a value

To modify the value of a constant you have to double-click on it to edit it. In the following case, the editionof a Boolean constant allows only the values True or False:

Using constants

The constants are used when the equations of the nodes are defined. They are handled like variables.

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3.13. Cost Management

BayesiaLab associates a cost to each node. This cost represents the price (in a scale shared by all thenodes) associated with the observation of the value of the node. It makes possible to carry out an ad-aptive questionnaire that sorts the questions in an optimal order with respect to the pertinence of thequestions with the current knowledge state (pertinence expressed in terms of information gain and as-sociated cost).

A node can also be declared as not observable. In this case, it will never appear in the adaptive ques-tionnaire; however, its value can be set manually by using its monitor. A not observable will not be ob-served either during the interactive inference and the Bayesian updating, nor during batch labelingor batch inference even if this node has a corresponding value in the associated database.

Cost table

The cost table can be edited by using the contextual menu associated to the graph or through the as-sistant of the adaptive questionnaire that is available in the Inference Menu Item.This table associatesa cost to each variable (1.0 is the default value). A cost must be superior or equal to 1. In order to indicatethat a variable is not observable, one has to delete the associated cost (or indicate a value inferior to1).


The costs can be edited individually for each node by using the contextual menu of the node, or byusing the thumbnail Properties of the node editor.

Import

The Import button allows importing a list of costs from a dictionary as in Import Dictionary menu.

Export

The Export button allows exporting the list of costs in a dictionary as in Export Dictionary menu.

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3.14. Forbidden arc management

It is possible to define forbidden arcs in a network, i.e. to prohibit the addition of arcs between two nodes,a node and a class, a class and a node and two classes.These forbidden arcs will be taken into accountduring the automatic learning of the networks' structure. Note that if an arc was added and it is definedas forbidden after, it will not be removed from the graph.

Forbidden arc editor

The forbidden arc editor is accessible by the contextual menu associated to the graph.The table showsthe list of the forbidden arcs with the starting node or class, the orientation that can be in one or bothdirections and the ending node or class.


In this example, you can see eight kinds of arcs constraints:

1. Forbidden arc from N1 to N2

2. Forbidden arc from N1 to N3 and from N3 to N1

3. Forbidden arcs from N1 to all the nodes of the class Class1

4. Forbidden arcs from N1 to all the nodes of the class Class2 and from all the nodes of the class Class2to N1

5. Forbidden arcs from all the nodes of the class Class1 to N2

6. Forbidden arcs from all the nodes of the class Class1 to N3 and from N3 to all the nodes of the classClass1

7. Forbidden arcs between the nodes of the class Class1

8. Forbidden arcs from all the nodes of the class Class1 to all the nodes of the class Class2 and fromall the nodes of the class Class2 to all the nodes of the class Class1

Add a forbidden arc

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The Add button displays the following dialog box to define a new constraint on the arcs. It is possible tochoose between a node and a class for the beginning and the end and to choose if the constraint appliesin one or both directions using the corresponding buttons:

Delete a forbidden arc

The Remove button deletes all the selected constraints in the table.

Import forbidden arcs

The Import button allows importing a list of forbidden arcs from a dictionary as in Import Dictionarymenu.

Export forbidden arcs

The Export button allows exporting the list of forbidden arcs in a dictionary as in Export Dictionarymenu.

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3.15. Temporal Indices

It is possible to associate a temporal indice to each node.This indice is a positive or null integer. It allowsindicating a temporal order between the nodes that is taken into account by the learning algorithms.

A node with a temporal indice greater than the temporal indice of another node cannot be its ancestor.

The editing of the temporal indices can be done node by node thanks to the node editor or globallythrough the contextual menu of the graph which gives access to the following global editor:


When at least one node has a temporal indice, the indicator is displayed in the status bar of thenetwork. A click on this icon displays the previous dialog box.

Import

The Import button allows importing a list of temporal indices from a dictionary as in Import Dictionarymenu.

Export

The Export button allows exporting the list of temporal indices in a dictionary as in Export Dictionarymenu.

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3.16. Structural Complexity Influence Coefficient

All the structural learning algorithms that are used in BayesiaLab are based on the Minimal DescriptionLength (MDL) principles. This score allows measuring the quality of the network with respect to thedatabase. It is made of two parts: one to score the structure, the other one to quantify how the networkfits data. The goal of the structural part is to implement the Occam criterion, i.e. the ones that allowschoosing the simplest hypothesis when all the other factors are identical. By default, the weights of thesetwo parts are identical.The parameter of the Structural Complexity influence makes it possible to changethe weight associated with the structural part. This parameter varies from 0 to 150. Whereas a weightequal to 0 implies a score entirely based on data fitting (the resulting structure can then be fully connec-ted), a weight equal to 150 favors simplest structures.This parameter is then as a significance threshold.The higher this factor is, the stronger the probabilistic relations have to be to have a corresponding arcin the network. Conversely, the lower the factor is, the weaker the probabilistic relation can be. It is thenparticularly useful when one does not have a lot of data. However, one has to take care of the significanceof the obtained probabilistic relations.

To measure the quality of the resulting network, it is possible to use a test database or to carry out anarc analysis.This analysis will return the weakest relation.Then, by using the occurrence matrix availablein the graph kit of BayesiaLab on the two involved variables of this weakest relation, one will get theChi2 value that tests the independence between these two variables. If this value is too low, one hasthen to increase the parameter.

When the coefficient is different from 1, the indicator is displayed in the status bar of the network.

The following editor can be accessed from the contextual menu of the network or from the indicator inthe status bar.

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3.17. Local Structural Coefficients

It is possible to associate a structural coefficient to each node. It has the same effect as the globalstructural coefficient but it acts only on the concerned node. This coefficient can vary between 0 and150. If there is no coefficient or if the coefficient is 1, there is no impact on the MDL score. When thecoefficient is less than 1, the learning algorithms will tend to increase the number of parents for this nodeand vice versa.

The editing of the local structural coefficients can be done node by node thanks to the node editor orglobally through the contextual menu of the graph which gives access to the following global editor:


When at least one node has a local structural coefficient, the indicator is displayed in the status barof the network. A click on this icon displays the previous dialog box.

Import

The Import button allows importing a list of local structural coefficients from a dictionary as in ImportDictionary menu.

Export

The Export button allows exporting the list of local structural coefficients in a dictionary as in ExportDictionary menu.

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3.18. State Virtual Numbers

It is possible to associate a state virtual number to each node. This index is integer greater or equal to2. It replaces the real number of states in the MDL score computation. In the same way as the localstructural coefficient, it allows increasing or decreasing the number of parents that will be linked tothe node during learning. A high number will decrease the number of added parents and vice versa.Contrary to the local structural coefficient, the state virtual number acts only on a part of the node's MDLscore computation.

The editing of the state virtual numbers can be done node by node thanks to the node editor or globallythrough the contextual menu of the graph which gives access to the following global editor:


When at least one node has a temporal index, the indicator is displayed in the status bar of thenetwork. A click on this icon displays the previous dialog box.

Import

The Import button allows importing a list of state virtual numbers from a dictionary as in Import Dictionarymenu.

Export

The Export button allows exporting the list of state virtual numbers in a dictionary as in Export Dictionarymenu.

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3.19. Experts

The assessment mechanism needs to define experts associated with the network.

An expert is defined by:

• a name that must be unique

• a credibility which is a real between 0 and 1.When an expert has its credibility equal to 0, his expertiseis not taken into account. A fully credible expert has a credibility of 1. This credibility weighs its ownexpertise relatively to others.

• an image for rapid identification. It can be a photo or an avatar for example.

• a comment which describes the expert (eg competence, domain, etc.)

In the editor expert, these four properties can be edited by double-clicking on the corresponding cell.The fifth property displayed is the number of assessments the expert has made in the network. Thisproperty is not editable.

The table can be sorted by clicking on the column headers.

Add :

The button Add opens a new window allowing the user to enter information about a new expert:

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To add or change the image, simply click in the box. The verification of the uniqueness of the name ismade during the validation.

Remove:

The button Remove the selected experts of the list. The assessment done by this expert will also beremoved from the nodes. However, the conditional probability tables won't be regenerated.

Import:

The button Import allows loading a dictionary of experts. The format of the dictionary is the following:

Structure of the dictionary file

Name of the expert, Equal, Space or Tab, credibility, Space, path of the image (optional),Space, //comment (optional). The path of the image is relative to the directory in which

Experts

the file is. In fact, it is more simple to put the images in the same directory. If the sameexpert is present sevral times, the last occurrence is always chosen.

Export:

The button Export exports a dictionary of experts.The images of the experts will be saved in png formatin the same directory as the dictionary with the name expertImageN.png

Open Session:

The button Open Session allows opening an online assessment session.

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The user msut provide a session identifier (unique) and a password. Once the session opened, the expertscan connect with their browser to the folowing secured address:https://www.bayesialab.com The usermust enter his name as given in the expert editor (respecting case) and the session identifier. To createan online assessment session, you must contact Bayesia directly: [email protected].

If a session with the same name has already been opened, a dialog box will offer to overwrite if thissession comes from the same machine. If it comes from another machine, it will not be possible to usethis session name.

Close Session:

the button Close Session allows ending the current online assessment session. Experts which arestill connected will be disconnected. Closing a network or BayesiaLab while a session is running auto-matically closes the session.

Generate Tables:

This button is active if at least one expert is selected. It generates conditional probability tables of thenodes by taking into account the assessment of selected experts. If none of the selected experts hasmade assessment for a node then the consensus of all experts is used.The credibility of experts is usedfor generation

When at least one expert is associated with the network, the indicator is displayed in the status barof the network. A clic on this icon displays this editor.

3.19.1. Assessment Report

This report is generated from the contextual menu of the expert icon in the status bar.

It contains two parts. The first part is a global summary analysis of the assessment:

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It shows the list of experts: their name, credibility, comment and the number of assessments done likein the expert editor.The last column shows the average assessment time used by each expert to makeassessment. This time is computed only when an online session is used.

After that, two tables are displayed:

• The first table is the list of the nodes with assessment.The first column is node name, the next columnis the comment of the node (depending on the settings) and the last one is the global disagreementof the assessments.This percentage represents the average deviation of each assessment with respectto the mean of each cell. It takes into account the confidence associated with each assessment. If anassessment has a confidence equal to zero, it won't be taken into account in the global disagreement.The nodes are sorted according to the global disagreement.

• The second table is also the list of the nodes with assessment. The first column is node name, thenext column is the comment of the node (depending on the settings) and the last one is the maximumdisagreement of the assessments. This percentage represents the maximum deviation of all assess-ments in the whole table. If an assessment has a confidence equal to zero, it won't be taken into accountin the maximum disagreement. The nodes are sorted according to the maximum disagreement.

The global and maximum disagreements between the experts allow us to easily find on which nodesthe knowledge of the experts is not the same and the knowledge elicitation should be verified.

The second part of the report details the assessment for each variable:

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For each node with assessment, a table contains:

• The number of rows in the conditional probability table that have assessments associated with comparedto the total number of rows

• The total number of assessments done on this node

• The number of experts involved compared to the total number of experts

• The global disagreement of the node

• The maximum disagreement in the conditional probability table

• The global assessment time which is the sum of all assessment times

• The mean assessment time by row of the conditional probability table

• The mean expert assessment time for this node

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3.20. Variations

Several analysis need to define positive and negative variations in order to apply them on the mean ofeach node. The following editor allows the user to edit these variations. This editor is accessible fromthe parameter panels of the concerned analysis. It is possible to associate with each node a negativeand a positive variation in percentage. These variations will be saved with the network and will beavailable for each analysis.

A variation, positive or negative, is a positive real number between 0 and 100%. The default value is10%.

The Import button allows importing a list of variations from a dictionary as in Associate Dictionarymenu. The syntax is:

Dictionary File Structure

Name of a node or a class Equal,Space orTabvariation for giving the same value to negative

Variations

and positive variations ornegative vari-ationSpacepositive variation for giving a differentvalue to negative and positive variations. Thevaraition is a real number between 0 and 100. Anode can be present only once otherwise the lastoccurrence is chosen.

Export

The Export button allows exporting the list of negative and positive variations in a dictionary as in ExportDictionary menu.

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3.21. Comments

It is possible to associate a comment to a network, to a node or to an arc by using the contextual menus.

Concerning the comments associated to the network, some actions add some fields to them automatically:

• The date and the author, when a network is created;

• The database, the number of lines, the value of the structural complexity if it differs from the defaultone, the missing value processing, the learning method, the final score and compression rate,at the end of learning.

Concerning the nodes, it is also possible to associate comments by using a dictionary file.The associatedcomments must be written in HTML (3.2) or in simple text. In this case, they will be automatically embed-ded inside and HTML document.

The comments associated to the nodes can be edited with the node editor.

The comments are in HTML (version 3.2).

The following editor allows creating complex comments in HTML.

The File menu allows :

• creating a new empty HTML document

• opening a HTML (3.2) file

• saving its comment in a HTML file

The Edit menu allows :

• copying, cutting and pasting

• undoing or redoing an action

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The Insert menu allows :

• inserting a link towards a file or an URL

• inserting an image

The Format menu allows :

• displaying the following dialog that allows modifying the page properties:

The Tools menu allows :

• displaying the HTML source of the comment that can be directly modified:

With the buttons of the toolbar, it is possible to change, for the current selection, the font, the textalignment, the bold, italic and underlined attributes and the color of the foreground and background.

According to the position of the cursor, the contextual menu, accessible with a right click, allows:

• copying or cutting the selection,

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• inserting, editing or removing a link,

• displaying page properties,

• displaying image properties

The nodes and the arcs that have an associated comment are presented as follows:

Comments are displayed by keeping pressed while pointing on the icon displayed on the nodeor the arc.To display the graph's comment the key must be pressed while hovering the graph's window.If a node has a color tag, the corresponding color is displayed as a border at the top and the left of thedisplay. A click on a hypertext link opens the associated document.

It is also possible to display all the comments in a specific window by using the contextual menu associ-ated to the network background. The contents of that window (HTML text) can then be copied&pastedto external applications, saved in a HTML file or printed.

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3.22. Contextual menus

The contextual menus are always available by a right click on the object.

On a node

• Edit (modeling mode): opens a dialog box for the edition of the node properties.

• Rename (modeling mode): allows editing the name of the corresponding node.

• Copy (any mode): allows copying the node (and the selection to which it belongs, if it exists).

• Delete (modeling mode): deletes the current node and all the selected ones.

• Set as Target Node (any mode): the target node (and its target value) is unique in the graph. It isused to supervise the Bayesian network learning algorithms in order to construct a structure dedicatedto the prediction of that node, or to indicate focusing the analysis on it.

• Influence Paths to Target (validation mode): shows the different influence paths that link the nodeand the target node.

• Monitor (validation mode): associates a monitor to this node and all the other selected nodes (seemonitor panel).

• Exclude (modeling mode): set the node as excluded so it won't be taken into account during learning.

• Graphs (any mode, with a database): shortcut to display the graphs editor with the selected nodesas entry variables (see graphs).

• Imputation (modeling mode, with a database and missing values): allows performing imputation ofthe missing values on the selected nodes if they are hidden or have missing values in the database.See database imputation.

• Follow the Temporal Evolution (any mode, dynamic Bayesian network): allows defining one orseveral states of a node for which the probability evolution will be followed during the temporal sim-ulation:

• Select:

• Connected Nodes: select the nodes that are directly or indirectly connected to this node.

• Connected Root Nodes: select the nodes that are directly or indirectly connected to this node andthat have no parent.

• Markov Blanket: select the nodes of this node's Markov blanket in the network.

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• Classes: select the nodes that belong to the same classes of this node.

• Alignment: aligns the set of selected nodes with respect to the node from which the contextual menuhas been activated:

• Horizontal (any mode): aligns the nodes by keeping their horizontal spacing.

• Vertical (any mode): aligns the nodes by keeping their vertical spacing.

• Horizontal Distribution (any mode): aligns the nodes and gives the same horizontal spacingbetween them.

• Vertical Distribution (any mode): aligns the nodes and gives the same vertical spacing betweenthem.

• Properties:

• Color: This property can be modified with the node editor.

• Edit (any mode): allows associating a color tag to the node and to all the selected nodes. Ifclasses are associated with these nodes, the chosen color can be associated with all the nodesof the selected classes.

• Remove (any mode): removes the color tagging of the node and of all the selected nodes. Ifclasses are associated with these nodes, colors can be removed from all the nodes of the selectedclasses.

• Image: This property can be modified with the node editor.

• Edit (any mode): allows associating an image to a node and to all the selected nodes that willbe displayed instead of the default node's view. If classes are associated with these nodes, thechosen image can be associated with all the nodes of the selected classes.

• Remove (any mode): removes the image of the node and of all the selected nodes. If classesare associated with these nodes, images can be removed from all the nodes of the selectedclasses.

• Classes: This property can be modified with the node editor or with the class editor.

• Add (any mode): allows adding an existing class or a new class to a node and to all the selectednodes.

• Remove (any mode): removes the selected classes from this node. If a removed class does notcontain any node, it will be deleted.

• Temporal Indice (modeling mode):This property can be modified with the node editor. It allows set-ting or removing the temporal indice of the node and of all the selected nodes. If classes are asso-ciated with these nodes, the temporal indices can be set or removed from all the nodes of the se-lected classes.

• Cost (any mode): This property can be modified with the node editor. It allows setting or removingthe cost of the node and of all the selected nodes. If classes are associated with these nodes, costsare set or removed from all the nodes of the selected classes.

• State Virtual Number (modeling mode): This property can be modified with the node editor. It al-lows setting or removing the sate virtual number of the node and of all the selected nodes. If classesare associated with these nodes, the state virtual numbers can be set or removed from all the nodesof the selected classes.

• Local Structural Coefficient (modeling mode):This property can be modified with the node editor.It allows setting or removing the local structural coefficient of the node and of all the selected nodes.

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If classes are associated with these nodes, the local structural coefficients can be set or removedfrom all the nodes of the selected classes.

• Exclusion (modeling mode):This property can be modified with the node editor. It allows excludingor not the node and all the selected nodes. If classes are associated with these nodes, all the nodesof the selected classes can be excluded or not.

• Comment (any mode): This property can be modified with the node editor.

• Edit (any mode): allows editing the comment of the node.

• Remove (any mode): removes the comment of the node and of all the selected nodes. If classesare associated with these nodes, images can be removed from all the nodes of the selectedclasses.

On an arc

• Change Orientation (modeling mode): inverts the arc. The probabilistic data associated with the twonodes are lost.

• Invert Orientation within the Equivalence Class (validation mode): inverts the arcs only if the res-ulting graph makes it possible to encode the same probability law. The conditional probability tablesof the implied nodes are automatically updated.These arc inversions are propagated to the other arcsand edges in order to preserve the probability law.

• Edge Orientation (validation mode): gives an orientation to an arc for which the orientation has pre-viously been removed (see edges display).

• Temporal Relation (any mode): defines the arc as a temporal arc; i.e. an arc with a particular semantic:the two linked nodes represent the same variable at two consecutive time steps. This is thanks to thisfunctionality that it is possible to define dynamic Bayesian networks.

• Delete (modeling mode): deletes the current arc and all the selected ones. The probabilistic data as-sociated to the destination node is lost.

• Properties:

• Color:

• Edit (any mode): allows associating a color tag to the arc and to all the selected arcs.

• Remove (any mode): removes the color tagging of the arc and of all the selected arcs.

• Fix (any mode): allows regarding the arc as a certain a priori knowledge for the Taboo learning al-gorithm (see learning), as well as in the edge orientation context.

• Comment (any mode):

• Edit (any mode): allows editing the comment of the arc.

• Remove (any mode): removes the comment of the node and of all the selected nodes. If classesare associated with these nodes, images can be removed from all the nodes of the selectedclasses.

On the background of the graph panel

• Copy the Selection (any mode): copy all the selected arcs and nodes.

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• Paste (modeling mode): paste the arcs and nodes previously copied inside the network, renamingthe nodes if necessary.

• Delete Selection (modeling mode): deletes all the selected arcs and nodes.

• Delete All Arcs (modeling mode): deletes all the arcs to obtain an unconnected network.

• Delete All Unfixed Arcs (modeling mode): deletes all the arcs that are not fixed.

• Delete All Unconnected Nodes (modeling mode): deletes all the nodes without any arcs.

• Delete All Virtually Unconnected Nodes (KL Force) (modeling mode): deletes all the nodes withoutany arcs (only if the Arc force analysis has occurred and the Arc force trim has been used in the val-idation mode: .

• Edit Structural Coefficient (any mode): opens the dialog box that allows modifying the structuralcomplexity influence coefficient of the network for learning.

• Edit Costs (any mode): opens the dialog box that allows associating a cost for the observation ofa variable (see Cost management).

• Edit Classes (any mode): opens the dialog box that allows the creation and the edition of theclasses associated to the nodes (see Classes management).

• Edit Constants (modeling mode): opens the dialog box that allows the creation and the edition ofthe constants that will be used in the formulas describing the probability distributions of the nodes(see Constants management).

• Edit the Forbidden Arcs (modeling mode): opens the dialog box that allows the creation of forbiddenarcs in the network's structure (seer Forbidden arcs management).

• Edit Temporal Indices (any mode) : opens the dialog box that allows editing the temporal indicesassociated to the nodes for learning.

• Edit State Virtual Numbers (modeling mode): opens the dialog box that allows editing the statevirtual numbers associated to nodes and used for learning.

• Edit Local Structural Coefficients (modeling mode): opens the dialog box that allows editing thelocal structural coefficients of each node. This coefficient is used for structural learning.

• Edit Experts (modeling mode): opens the dialog box that allows editing the experts of the network.Experts are used for assessment sessions.

• Use Time Variable (modeling mode): allows using the parameter variable that represents the timein the equations.

• Display Comments: allows displaying all the comments into a specific window.

• Graph Report: allows displaying a report containing some properties of the network (like connectivity,number of nodes, of arcs, etc.) and also the different warnings and errors of the nodes. This reportalso contains the conditional probability tables of the selected nodes. If there is no selected node, allthe tables are displayed. A list of the excluded nodes and a sorted list of the forbidden arcs areadded if necessary.

• Properties:

• Background Image:

• Edit (any mode): allows the selection of an image file in order to set it as background of the currentgraph window. It is possible, through the settings, to activate or deactivate this functionality.

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• Remove (any mode): removes the image from the background of the active graph window.

• Font: allows changing the font used to display the nodes' name.

• Comment: allows adding a comment to the network. A default comment with the date and authorname is automatically associated at the creation of a network. The comment is displayed whenpressing while pointing on the background of the graph panel.

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4. Monitor panel

In Validation mode, a graph window presents two panels: the graph panel and the monitor panel. Themonitor panel is used to visualize the probability distributions of the monitored variables returned by theinference process. It is also the panel that easily allows entering evidences (hard and soft) about thevariables.

4.1. Monitor use

Functions

A monitor associated with a node allows:

1. displaying the marginal probability distribution of the node, taking into account the knowledge encodedby the network and the evidences entered for the other nodes, if any. The monitor gives the probab-ility distribution of the node by using bars that are proportional to the probabilities. The numericalvalues of these probabilities are also given in percentages or with scientific notation if the option ischosen in the monitor's contextual menu . If the displayed value corresponds to the exact one, itis displayed with bold face . Keeping the key pressed while pointing on the monitor show a tooltipcontaining the exact values.With continuous node or discrete node with numerical states, the monitorgives the mean and standard deviation and offers a richer graphical display by using the contextualmenu (relative charts, as illustrated below). This display is not available with utility nodes.

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2. entering evidences (hard or soft) about the variable. Each observation/removal causes the dynamicupdate of the displayed monitors.

The monitors that are associated with Utility nodes are used to display the expected value of the nodeand the sum of expected utilities.

The monitors associated with Decision nodes are used to display the marginal probabilities of the de-cision, to indicate what the optimal action is, and to choose the action to apply.

Creation

It is only possible to associate a monitor with a node in Validation mode. BayesiaLab offers two waysto create monitors:

1. a double-click on the node,

2. via the contextual menu of the node

The monitor then appears displayed in the monitor panel.

Removal

There are four possibilities to delete a monitor:

1. a double-click on the corresponding node,

2. via the contextual menu associated with the node,

3. via the contextual menu associated with the monitor,

4. by selecting the monitor and by pressing the key.

States

A monitor can be in different states, depending on the type and the state of the associated node:

1. normal: probability distribution of a chance node;

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2. hard evidence : the observed value is highlighted with the green bar;

3. setting soft evidences : allows entering a likelihood for each state;

4. soft evidences validated: after validating soft evidences with the light green button;

5. setting probabilities: allows entering a probability for each state;

6. likelihoods validated from probabilities: after validating probabilities with the light green button;

7. fixed probabilities validated: after validating probabilities with the mauve button;

8. target: probability distribution of the target node;

9. target + targeted value: probability distribution of the target node within the framework of an adaptivequestionnaire centered on a target value. The target value probability appears in light blue;

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10. temporal: probability distribution of a temporal father node (current time step);

11. utility: expected value of the utility node and the sum of all the expected utilities (in bold face). Thesevalues appear with their respective minimal and maximal values.

12. decision: displays the probability distribution of the actions corresponding to a decision node (equi-probable except when descendant nodes are observed). The recommended action with respect tothe context appears in light blue. This action corresponds to the one with the best expected quality,quality that can be displayed by pressing the key while pointing on the monitor

13. not observable: there is no cost associated with the node, it won't be proposed in the adaptivequestionnaire and it won't be observed in the interactive inference, the interactive updating, thebatch labeling and the batch inference.

14. causal : probability distribution of a causal node.

Displaying colored tags

If the node associated with the monitor has a colored tag and the colors display is activated with thebutton , this color is displayed in the monitor's border:

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Displaying target state indicator

If the node associated with the monitor is the target node, its target state will be indicated with the icon:

Displaying filtered state indicator

If the node has a filtered state then the icon will indicate the corresponding state:

Setting/removal of hard evidence (observation)

The observation, or the removal of the observation of a variable, also called hard evidence, is carriedout either by double-clicking on the desired value, or by the means of the contextual menu associatedwith the monitor.

Setting hard evidence gives:

The observed node takes the green color of the observation.

Soft Evidence setting (likelihood)

Soft evidences are evidences that enable to modify the probability distribution of a node. The resultingrelative likelihoods allow then computing, for each state, a factor used to update the probability distribution.

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A node state with a zero likelihood value is an impossible state. If all the states have the same likelihood,the probability distribution remains unchanged.

The soft evidence edition mode is available by two means: by pressing the key while clicking on astate bar or by using the contextual menu associated with the monitor. A green and red buttons arethen added to the monitor. The likelihoods can be entered:

• by maintaining the left mouse button pressed while choosing the desired likelihood level, or

• directly by editing the likelihood value by double-clicking on the value.

Once all the likelihoods are entered, the light green button allows validating the data entry and theprobability distribution is updated. The red button allows cancelling the likelihood edition.

Setting likelihoods:

Result after validating with the light green button:

The observed node takes the light green color of the evidence.

Probability Setting

Setting the probabilities allows directly indicating the probability distribution of a node. Likelihoods arerecomputed so that the final probability distribution of the node is the same as entered by the user.

The probability edition mode is available by two means: by pressing the and keys while clickingon a state bar or by using the contextual menu associated with the monitor. A light green, mauve andred buttons are then added to the monitor. The probabilities can be entered:

• by maintaining the left mouse button pressed while choosing the desired probability level, or

• directly by editing the probability value by double-clicking on the value.

• A click on the name of the state (on the right) fix the current probability value (the probability bar isgreen).

Once all the probabilities are entered, the light green button allows setting the probabilities and themauve button allows fixing the probabilities. The probability distribution is then updated. The redbutton allows cancelling the probability edition.

So, there are two ways to use the probability capture:

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1. Simply setting the probabilities: When the probabilities are validated with the light green button,the likelihoods associated with the states of the node are computed again in order to make the mar-ginal probability distribution correspond to the distribution entered by the user. It is, in fact, an indirectcapture of the likelihoods.You must note that, at the next observation of another node, the probabilitydistribution of this node will change because the likelihoods are not computed again.The result willbe displayed with light green bars as the likelihoods:

The observed node takes the light green color of the evidence.

2. Fixing the probabilities: When the probabilities are validated with the mauve button, the likelihoodsassociated with the states of the node are computed again in order to make the marginal probabilitydistribution correspond to the distribution entered by the user, as in the previous case. However, ateach new observation on another node, a specific algorithm will try again to make the probabilitydistribution of the node converge towards the distribution entered by the user. Fixing probabilities isalso done in the evidence scenario files with the notation p{...}.You must note that fixing probabilitiesis only valid for the exact inference. If the approximate inference is used, fixing probabilities is con-sidered like simply setting the probabilities: there is no more convergence algorithm.The result willbe displayed with mauve bars:

The observed node takes the mauve color of the evidence.

Caution

To obtain the indicated distribution, a convergence algorithm is used. However, sometimesthis algorithm cannot converge towards the target distribution. In this case, the probabil-ities fixing is not done and the node comes back to its initial state. In this case a warningdialog box is displayed and an information message is also written in the console.

Setting a target mean/value

When a node has values associated with states or is a continuous node or has numerical states, it ispossible to choose a target mean/value for this node. An algorithm based on MinXEnt allows determininga probability distribution corresponding to this target mean/value, if this distribution exists. Of course,the indicated target value must be greater than or equal to the minimum value and less than or equalto the maximum value.

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Once the target value entered, there are three options:

• No Fixing: the distribution found must be observed as likelihoods.

• Fix Mean: the indicated mean must be observed as fixed mean. When the mean is fixed, if an obser-vation is done on another node, the convergence algorithm will automatically determine a new distri-bution in order to obtain the target mean, taking the other observations into account. If we store thisevidence in the evidence scenario file, only the target mean will be stored. Fixing mean is also donein the evidence scenario files with the notation m{...}. You must note that fixing mean is only validfor the exact inference. If the approximate inference is used, fixing mean is considered like simplysetting the likelihoods corresponding to the target mean: there is no more convergence algorithm.

• Fix Probabilities: the distribution found must be set as fixed probability distribution. Fixing probabilitiesis also done in the evidence scenario files with the notation p{...}. You must note that fixing probab-ilities is only valid for the exact inference. If the approximate inference is used, fixing probabilities isconsidered like simply setting the likelihoods corresponding to the target mean: there is no moreconvergence algorithm.

Fix Current Probabilities

It is possible to quickly fix the current probability distributions of the selected nodes by using the contex-tual menu. All the selected nodes will have their own current marginal probabilities as fixed probabilities.

Negative Evidence Setting

It is possible to quickly indicate an impossible value (zero likelihood value) by maintaining the keypressed while double clicking on the state that is impossible.

Selecting evidence in the evidence scenario file

When an evidence scenario file is associated with the network, the icon is displayed in the network'sstatus bar. In validation mode, a right click on this icon displays a list of the evidence sets contained inthe evidence file:

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Simply click on one of the evidence sets in order to set the corresponding observations (if it is possible).This option is disabled in temporal networks and during interactive inference and updating.

Selecting evidence in the database

When a database is associated with the network and has row indentifiers, a right-click on the databaseicon in the status bar, in validation mode, displays a panel allowing the user to perform a search amongthe row identifiers. The search is done thanks to a text field. The wildcards characters ? and * can beused. ? can replace one and only one character. * can replace none or several characters. The CaseSensitive option allows the search to respect the case. After pressing enter, the search is performedand the list of the results is displayed. The number of corresponding rows is displayed at the bottom ofthe panel. A click on a line sets the corresponding observations:

At each example, the nodes are observed with the corresponding value in the database except if thisvalue is missing or the nodes are declared as not observable or as target. This option is disabled intemporal networks and during interactive inference and updating.

Soft Evidence Removal

Soft evidences can be removed by using the contextual menu.

Target Node definition

It is possible to quickly indicate the target node and its target state by maintaining the key pressedwhile double clicking on the target state of the node. A double click on the current target state allows tothe remove the target property from that node.

Node centering

Pressing key pressed while clicking on monitor, or on the selected monitor, allows centering thegraph on the associated node and makes that node blinking during a few seconds.

Node selection

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Pressing key pressed while clicking on monitor, or on the selected monitor, allows selecting thecorresponding node.

Monitor list

The list of the monitors can be reordered by drag&drop.

Exact Probability Values

The probabilities that are displayed in the monitors can be rounded. When they are exact, they appearin Bold face. However, it is always possible to display the exact probabilities by using the shortcutwhen focusing on the monitor.

Probability Variation

This option allows visualizing the variation of the probabilities between each modification of the set ofevidences.

A double-click on the monitor, outside the state zone, or pressing the button allows resetting the arrows.

The button of the monitor's toolbar allows specifying the current probability distributions as the referencestate for the computation of the probability variation. The reset of the arrows is then unavailable.

The button displays the maximum positive variation and the maximum negative variation among allthe states of all the nodes.

Displaying computed value

When a node has values associated with its states, the resulting value, computed according to theprobability distribution, is displayed. If the node doesn't have any values associated, if the node is con-tinuous the mean of each interval (computed from the data if a database is associated or the arithmeticalmean is taken) is used, otherwise if the node is discrete with integer or real values, these ones are used.The option allows, as for the probabilities variations, visualizing the value variations between eachmodification of the evidence set. These variations are displayed at the right of the value.

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Displaying monitor's tooltip

By pressing the key and moving the cursor over a monitor, a tooltip containing information about themonitor is displayed.

It contains the comment of the node if any or the name of the node if the comment is displayed insteadof the name in the monitor. It contains a table with the states' names as first column, the correspondingprobabilities as second one and the number of cases each state represents according to evidences.This last column is displayed only when a database is associated with the network.

Copy&Paste

Monitors can be copied and pasted to external applications.They can be pasted as images or data arraysin plain text or in html format. In addition to the probabilities, the mean, standard-deviation and valueare also copied if they are present.

Zoom

Monitors can be zoomed or unzoomed up to the convenient buttons in the monitor toolbar.

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4.2. Monitor contextual menus

On the background of the monitor panel

• Monitors sorted wrt Target Variable Correlations: displays the monitors sorted wrt the target variablecorrelations. If a subset of nodes is selected in the graph, this function is restricted to the monitors ofthose nodes. If some nodes are translucent, their monitors are not displayed.

• Monitors sorted wrt Target Value Correlations: displays the monitors sorted wrt the target valuecorrelations. If a subset of nodes is selected in the graph, this function is restricted to the monitors ofthose nodes. If some nodes are translucent, their monitors are not displayed.

• Sort by Less Probable Evidence: displays the monitors corresponding to the observed nodes fromthe less probable evidence (that degrades the most the joint probability) to the most probable evidence.

• Sort Monitors by Name: displays the monitors under increasing lexicographic order of their namesor comments (if comments are displayed instead of names).

• Remove All Observations: removes all the observations.

• Delete All: deletes all the monitors.

• Select All: selects all the monitors.

• Display Comment Instead of Name: displays the comment associated with the node instead of thename in the monitor. If the comment is too long, it will be truncated like the name would be.This optionis saved with the network.

• Display the States' Long Name: displays the long name eventually associated with the nodes' statesinstead of the states' name. When a state does not have a long name associated, its own name isused instead. If the long name is too long, it will be truncated as the states' name would be.This optionis saved with the network.

• Display Probabilities with Scientific Notation: displays the probabilities in scientific notation in themonitors and in the monitors' tooltips. This option is saved with the network.

• Fit Monitor Widths to Content: enlarge the monitors in order to display the whole content withoutcropping the names. This action is done only on the displayed monitors. If a new monitor is displayedand its width is greater, you must click on it again.

• Restore Default Monitor Widths: restore the witdh of the monitors to the default value.

• Display the Uncertainty and Likelihood Variations: displays in the information panel the uncertaintyand likelihood variations due to the evidences that were set.

• Print: launches the printing assistant that allows printing the monitors.

On the monitor

The monitor contextual menu is dynamic. It depends on the type and the number of states of the monitorednode.

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• Enter Likelihoods: allows entering in the soft evidence entry mode.

• Enter Probabilities: allows entering in the probability entry mode.

• Distribution for Target Value/Mean: allows entering a target mean/value and the correspondingprobability distribution will be automatically determined, if it exists. This menu is always available forthe continuous nodes and for the discret nodes having values associated to their states or if theirstates are numbers.

• Fix Probabilities: allows fixing the probabilities of the selected nodes to the current marginal probab-ilities.

• Absolute and relative bars and relative curve: allows changing the display mode of the chart thatrepresents the marginal probability distributions. These menus are not available on utility nodes.

• Remove Likelihoods: allows removing the evidence entered by the user whatever the kind of evidenceused. This option is only available when the node is observed.

• State List: a click on a state in this menu selects/unselects an observation of this state.

• Copy: copies the selected monitors into the clipboard, allowing pasting them into word processingsoftware for example.

• Delete: deletes the selected monitors. However, the states of the nodes (observed or not) remainunchanged.

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5. Shortcuts

Create a new Bayesian network +

Open a file +

Save the active Bayesian network +

Close the active graph window +

Print the active Bayesian network +

Export the active Bayesian network +

Undo +

Redo +

In the graph's window: Select all the nodes and arcsIn the monitors' window: select all the monitors

+

Copy the selected objects to the clipboard. Theseobjects can then be pasted in BayesiaLab or in ex-

+

ternal applications (nodes and arcs, conditionalprobability tables, equations, graphs, confusionmatrix, monitors)

Paste the copied objects + (Modeling mode)

Cut the selected objects + (Modeling mode)

Search for nodes, arcs and monitors +

Zoom in and out or

Default Zoom +

Adjust and optimize the size of the network to fit thewindow

+

Zoom in or out the network + mouse wheel on the network

Rotate counterclockwise or clockwise the network or

Center the network in the working window +

Horizontal or vertical flip + or

Put the network in the upper left corner of theworking window

+

Add the pointed object to the selection + Click (Modeling mode)

Move the network in the graph window + Drag

Close BayesiaLab +

Move an arc + Drag

Zoom in or out the monitors + mouse wheel on the monitors

Define the corresponding node and state as targets + double-click on a state of a monitor (Validationmode)

Enter the Soft-Evidence Edition mode + click on a state of a monitor (Validation mode)

Enter the Probability Edition mode + + click on a state of a monitor (Validationmode)

Center the node corresponding to the selectedmonitor

+ click on a monitor (Validation mode)

Select the node corresponding to the selectedmonitor

+ click on a monitor (Validation mode)

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Show edges (Validation mode)

Arc Force Analysis (Validation mode)

Pearson's Correlation Analysis (Validation mode)

Node Force Analysis (Validation mode)

Hides or displays the various node's indicators + +

Displays the comments associated to a node ifpressed while hovering on the node or arc's com-ment indicator. Displays the warning or error mes-sage if pressed while hovering over the node's errorindicator. Displays the number of missing values ifpressed while hovering over the node's missingvalues indicator. Displays the probability exact val-ues if pressed while hovering over a monitor.

Influence Analysis wrt Target Node + (Validation mode)

Mosaic Analysis + (Validation mode)

Global Orientation of edges (Validation mode)

Target Dynamic Profile + (Validation mode)

Generate the target node analysis report (Validation mode)

Generate the evidence analysis report + (Validation mode)

Generate the relationships analysis report + (Validation mode)

Variable Clustering (Validation mode)

Select and center the nodes corresponding to theselected monitors.

(Validation mode and monitors selected)

Total Effects on Target + (Validation mode)

Target Mean Analysis (Validation mode)

Switch to the Decision Node Creation mode whilethe key is pressed

(Modeling mode)

Switch to the Constraint Node Creation mode whilethe key is pressed

(Modeling mode)

Switch to the Deletion mode while the key ispressed

(Modeling mode)

Display or not the positioning grid +

Display or not the images associated to the nodes +

Switch to the Arc Creation mode while the key ispressed

(Modeling mode)

Switch on/off the node comments

Switch on/off the arc comments +

Switch to the Node Creation mode while the key ispressed

(Modeling mode)

Set or not the node and its first state as target de-pending on its current state.

+ double-click on a node

Display or not the colored tags on the nodes +

Switch to the Utility Node Creation mode while thekey is pressed

(Modeling mode)

Display the network's comment if pressed whilehovering the background of the graph

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Exclude or include the node depending on its cur-rent state.

+ double-click on a node (Modeling mode)

Switch to the Selection mode while the key ispressed

(Modeling mode)

Delete the selected objects: nodes and arcs inModeling mode and monitors in Validation mode

Quick automatic positioning of the nodes

Display this help document

Activate the contextual help

Switch to modeling Mode

Switch to Validation Mode

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Chapter III. MenusThis section describes the BayesiaLab's menus.

When there is no opened graph window, the menu bar is made of only five principal items:

• Network: for the opening or the creation of a network

• Data: for the creation of a network corresponding to a data base

• Tools : for the comparison of networks

• Options: for the console management and general BayesiaLab settings

• Help: for different functions concerning BayesiaLab.

Once a graph window is opened, the menu bar is completed by six other items:

• Edit: for the graphical edition of the graph

• View: for the management of the graph display in the graph window.

• Learning: for the automatic network modeling with respect to a database.

• Inference: for the adaptive questionnaire, batch exploitation or the choice of the type of inference.

• Analysis: for the specification of analysis options, and for network evaluation. Visible in validationmode only.

• Monitor: for managing the monitors in validation mode. Visible in validation mode only.

• Tools: for several tools on networks.

1. Network

• New: creates a new graph window.

• Open: reads a file (XBL, BIF, NET or DNE formats) and opens a new graph window containing theBayesian network described in this file.There are three icons that can be displayed in the file chooser:

• If the selected network has a database associated to it, then this option proposes to load thisdatabase with the network or not.

•

• If the selected network has an evidence scenario file associated to it, then this option proposesto load this file with the network or not.

• If the selected network has its junction tree saved with it, then this option proposes to load thejunction tree with the network or not.

• Save: saves the Bayesian network of the active graph window using the XBL format. If the networkhas a database or/and an evidence scenario file associated to it, they will be saved in the same fileas the network in order to load them later.These features can be cancelled in the database settings.If the network as a junction tree, it will be also automatically saved in the same file.

• Save As: saves the Bayesian network of the active graph window with a specified name. There arethree icons that can be available in the file chooser:

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• If the network has a database associated to it, then this option proposes to save this databasewith the network or not.

•

• If the network has an evidence scenario file associated to it, then this option proposes to savethis file with the network or not.

• If the network has a junction tree created, then this option proposes to save the junction tree withthe network or not

• Close: closes the active graph window. Proposes to save the network, the associated database andevidence scenario file if one of them is modified.

• Close All: closes all the graphs, prompting for saving the network, the associated database andevidence scenario file if one of them is modified.

• Recent Networks: keeps a list of the recently opened networks. The size of this list can be modifiedthrough the settings of menus. If a network is loaded from this list, the associated database, evidencescenario file and junction tree will be automatically loaded.

• Choose Working Directory: allows indicating in which directory we want to work. A name is associatedto this directory and it is added to the list of recent working directories.The following dialog box allowsconfiguring it:

The directory changing policy can be modified in the directory preferences.

• Recent Working Directories: keeps a list of the recent created or used working directories.

• Export: allows exporting the Markov blanket of the target variable of the current network intoa language selected in the following dialog box:

Once the network is exported in a language, it can be used to infer the value of the target variableaccording to the observations of the other variables.

• Lock: allows locking the network with a password to prevent it from editing. The network can beused only in validating mode. This menu gives access to lock manager.

• Print: prints the Bayesian network of the active graph window. An assistant gives access to:

• the setup of the page-setting,

• the configuration of the printer,

• the selection of the desire scale for the network,

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• the possibility of displaying reference marks. These marks are useful when the network has to beprint on more than one page. They indicate the page number (column, row), the border, and thevicinity,

• the possibility to center the network.

• Exit: Closes all the graphs, prompting for saving if needed, and closes BayesiaLab.

1.1. Network export

It is possible to export, under various languages, the Markov Blanket of the network's target in order tointegrate it in other software to do prediction. To export the network, a target must be defined before.After that, simply choose the export language in the following dialog box:

Several export languages are available according to the options of your license. If you need otherlanguages, you must update your license. It is also possible to ask Bayesia to develop other exportformats that have not been already taken in account. Some of these export formats exist but are onlyused by Bayesia SA. You can contact us to see the conditions for that Bayesia generates the corres-ponding outputs.

The Settings button can display a dialog box allowing specifying the options depending on the selectedlanguage.

SAS

This format is available with the convenient license.

JavaScript

This format belongs to Bayesia S.A. To export under this language, please contact us.

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PHP

This format belongs to Bayesia S.A. To export under this language, please contact us.

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1.2. Network Locking

It is possible to prevent a network from editing in order to use it only in validating mode.

A locking mechanism with password forbids the editing of a network previously locked. It allows the userto distribute its network to other users to only perform inference, preventing the network fromany modification.

When a network is locked, it is no more possible to edit the nodes and their properties (the modificationsare not taken into account), to add or delete arcs and nodes, to associate dictionaries and databasesfor learning, to modify classes, etc.

However, it is always possible to modify the costs associated to the nodes because they are use invalidating mode (adaptive questionnaire, not observable nodes, etc.).

Adding a lock to the network is done through the menu Network>Lock.When the network doesn't alreadyhave a lock, the following dialog box is displayed:

You have simply to enter a password and to confirm it. Then, the indicator is displayed in the statusbar of the network. The network has a lock, now, but it is still modifiable because it is not locked. Toprevent editing, you have just to click on the indicator in order to become . This icon indicates that thenetwork is not editable anymore. To be able to edit it again, simply click on the icon (or with themenu Network>Lock) and a dialog box asking the password is displayed:

When the network is unlocked, the menu Network>Lock displays the following dialog box:

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This dialog box allows the user to:

• lock the network using the existing password

• remove completely the lock

• change the lock password.

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2. Data

• Open data source: This menu item allows opening the file or the database selector and then callsthe Data importation wizard .

• Text file: Once the file is read and the pre-processing done, a fully unconnected network is createdin a new graph window, each attribute having one corresponding node.The set of Bayesian networklearning methods becomes then available.

• Database: Once the database table is loaded and the pre-processing done, a fully unconnectednetwork is created in a new graph window, each attribute having one corresponding node. The setof Bayesian network learning methods becomes then available.

• Recent databases: Keep a list of the recently opened databases. The Data importation wizardis directly opened on the selected file. The size of this list can be modified through the settingsMenus .

• Associate data source: This menu item allows opening the Data association wizard in order toassociate data from a text file or a database with an existing Bayesian network.

• Recent databases: Keep a list of the recently opened databases. The Data association wizardis directly opened on the selected file. The size of this list can be modified through the settingsMenus .

Warning: When the network structure is modified during the association (addition of nodes or states),the conditional probability tables are automatically recomputed from the database. If the structure re-mains unmodified, the conditional probability tables are not modified.

• Associate dictionary: This menu item allows defining the properties of the active Bayesian networkthanks to text files. These properties concern arcs, nodes and states:

• Arc:

• Arcs: allows associating a set of arcs to the network.The indicated arcs can be added or removedfrom the network. The arc removal will always be done before adding an arc. Before adding anarc, all the constraints belonging to the Bayesian network as well as the arc constraints and thetemporal indices will be checked. If a constraint is not verified, then the arc won't be added.

• Forbidden Arcs: allows associating with the network a set of forbidden arcs .

• Arc Comments: allows associating with the network a set of arc comments .

• Arc Colors: allows associating with the network a set of colors on the arcs.

• Fixed Arcs: allows defining if some arcs are fixed or not.

• Node:

• Node Renaming: allows renaming each node with a new name. These new names must be, ofcourse, all different.

• Comments: allows associating a comment with each node that is in the file.

• Classes: allows organizing nodes in subsets called classes . A node can belong to severalclasses at the same time.These classes allow generalizing some node's properties to the nodesbelonging to the same classes. They allow also creating constraints over the arc creation duringlearning.

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• Colors: allows associating colors with the nodes or classes that are in the file. The colors arewritten as Red Green Blue with 8 bits by channel in hexadecimal format (web format): for examplethe color red is 255 red 0 green 0 blue, it will give FF0000. Green gives 00FF00, yellow givesFFFF00, etc.

• Images: allows associating colors with the nodes or classes that are in the file. The images arerepresented by their path relatively to the directory where the dictionary is.

• Costs: allows associating with each node a cost . A node without cost is called not observable.

• Temporal Indices: allows associating temporal indices with the nodes that are in the file.Thesetemporal indexes are used by the BayesiaLab's learning algorithms to take into account anyconstraints over the probabilistic relations, as for example the no adding arcs between futurenodes to past nodes. The rule that is used to add an arc from node N1 to node N2 is:

• If the temporal index of N1 is positive or null, then the arc from N1 to N2 is only possible if thetemporal index of N2 is greater of equal to the index of N1.

• Local Structural Coefficients: allows setting the local structural coefficient of each specifiednode or each node of each specified class.

• State Virtual Numbers: allows setting the state virtual number of each specified node or eachnode of each specified class.

• Locations: allows setting the position of each node.

• State:

• State Renaming: allows renaming each state of each node with a new name.

• State Values: allows associating with each state of each node a numerical value .

• State Long Names: allows associating with each state of each node a long name more explicitthan the default state name. This name can be used in the different ways to export a database,in the html reports and in the monitors.

• Filtered States: allows defining a state to each node as a filtered state .

Dictionary File Structures

Name of the arc's starting node or class, -> , <- or even -- toindicate the both possible orientations, name of the arc's

ArcsArc

ending node or class, Equal, Space or Tab , true for an addedarc or false for a removed arc. The last occurrence is alwayschosen.

Name of the arc's starting node or class, -> , <- or even -- toindicate the both possible orientations, name of the arc'sending node or class.

Forbidden Arcs


Comments

ending node or class, Equal, Space or Tab , comment . Thecomment can be any character string without return (in htmlor not). The last occurrence is always chosen.


Colors

ending node or class, Equal, Space or Tab , color .The coloris defined as Red Green Blue 8 bits by channel color writtenin hexadecimal (web format). For example green gives

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00FF00, yellow gives FFFF00, blue gives 0000FF, pink givesFFC0FF,etc. The last occurrence is always chosen.


Fixed Arcs

ending node or class, Equal, Space or Tab , true for an fixedarc or false for a not fixed arc. The last occurrence is alwayschosen.

Name of the node Equal,Space or Tab new node name. Thenew name must be valid (different from t or T and without?).

Node RenamingNode

A node can be present only once otherwise the last occur-rence is chosen.

Name of the node or the class Equal, Space or Tab Comment.The comment can be any character string without return (in

Comments

html or not). A node can be present only once otherwise thelast occurrence is chosen.

Name of the node Equal,Space or Tab Name of the class.The class can be any character string. A node can be presentseveral times associated with different class names.

Classes

Name of a node or a class Equal,Space or Tab Color Thecolor is defined as Red Green Blue 8 bits by channel color

Colors

written in hexadecimal (web format). For example green gives00FF00, yellow gives FFFF00, blue gives 0000FF, pink givesFFC0FF, etc. A node can be present only once otherwise thelast occurrence is chosen.

Name of a node or a class Equal,Space or Tab path to theimage relatively to the directory where the dictionary is. The

Images

image path must be a valid relative path or an empty string.A node can be present only once otherwise the last occur-rence is chosen.

Name of the node Equal,Space or Tab value of the cost orempty if we want the node to be not observable. The cost is

Costs

an empty string or a real number superior or equal to 1. Anode can be present only once otherwise the last occurrenceis chosen.

Name of the node Equal,Space or Tab value of the index orempty if we want to delete an already existent index The index

Temporal Indices

is an integer. A node can be present only once otherwise thelast occurrence is chosen.

Name of the node Equal,Space or Tab value of the localstructural coefficient or empty if we want to reset to the default

Local Structural Coeffi-cients

value 1. The local structural coefficient is an empty stringor a real number superior to 0. A node can be present onlyonce otherwise the last occurrence is chosen.

Name of the node Equal,Space or Tab virtual number of statesor empty if we want to delete an already existent number.The

State Virtual Numbers

state virtual number is an empty string or an integer superioror equal to 2. A node can be present only once otherwise thelast occurrence is chosen.

Name of the node Equal,Space or Tab , position.The locationis represented by two real numbers separated by a Space .

Locations

The first number represent the x-coordinate of the node and

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the second number the y-coordinate. A node can be presentonly once otherwise the last occurrence is chosen.

Name of the node or class dot (.) name of the stateEqual,Space or Tab new state name or State

State RenamingState

nameEqual,Space or Tab new state name if we want to re-name the state for all nodes. The new name is a valid statename. A state can be present only once otherwise the lastoccurrence is chosen.

Name of the node or class dot (.) name of the state Space orTab real value or Name of the state Equal,Space or Tab real

State Values

value if we want to associate a value with a state whateverthe node. The value is a real number. A state can be presentonly once otherwise the last occurrence is chosen.

Name of the node or class dot (.) name of the stateEqual,Space or Tab long name or Name of the state

State Long Names

Equal,Space or Tab long name if we want to associate a longname with a state whatever the node. The long name is astring. A state can be present only once otherwise the lastoccurrence is chosen.

Name of the node or class dot (.) name of the filtered state.A state can be present only once otherwise the last occur-rence is chosen.

Filtered States

Caution

As indicated by the syntax, the name of the node, class or state in the text file cannotcontain equal, space or tab characters. If the node names contain such characters in thenetworks, those characters must be written with a \ (backslash) character before in thetext file: for example the node named Visit Asia will be written Visit\ Asia in the file.

Caution

In order to specifically differenciate a nam which is the same for a classe, a node or astate, you must add at the end of the name the suffix "c" for a class, "n" for a node and"s" for a state.

Important

If your network contains not-ASCII characters, you must save your own dictionaries withUTF-8 (Unicode) encoding. For example, in MS Excel, choose "save as" and select "TextUnicode (*.txt)" as type of file. In Notepad, choose "save as" and select "UTF-8" as encod-ing. If your file contains only ASCII character you can let the default encoding (dependingon the platform) but it is strongly encouraged to use UTF-8 (Unicode) encoding in orderto create dictionary files that doesn't depend on the user's platform. So, for example, achinese dictionary can be read by a german without any problem whatever the usedplatforms are. If you are not sure how to save a file with UTF-8 encoding, you should exporta dictionary with BayesiaLab, modify and save it (with any text editor) and load it inBayesiaLab.

• Export dictionary: This menu item allows exporting the different kinds of dictionaries in text files.

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Important

The dictionary files are saved with UTF-8 (Unicode) encoding in order to support anycharacter of any language. An option, in the Import and Associate preferences: SaveFormat , allows saving or not the BOM (Byte Order Mask) at the beginning of the file.The BOM increases the compatibility with Microsoft applications. On other platform likeUnix, Linux or Mac OS X, the BOM is not necessary and, in come cases, is consideredas simple extra characters at the beginning of the file.

• Associate an evidence scenario file: This menu item allows associating an evidence scenario filewith the network.

• Export an evidence scenario file: This menu item allows exporting into a text file an evidencescenario file associated with the network.

• Generate data :This menu item allows generating a base of n cases in agreement with the probabilitylaw described by the active Bayesian network. It is possible to choose to generate the data as an in-ternal database. We can also indicate the rate of missing values of the base and use the long nameof the states if the database is written in a file. It is possible to generate a database with test examplesby indicating the wanted percentage.

The states' long name can be saved instead of the states' name. If the user wants to save the continu-ous values, the numerical values will be created by randomly generating a value in each concernedinterval. If the data are generated in validation mode , then the evidences are taken into account.

• Save data : This menu item allows saving the base associated with the network including the resultsof the various pre-processing that have been carried out within the data importation wizard (discret-ization, aggregation, filtering,). If the imported database still contains missing values and if the selectedalgorithm to process the missing values is one of the two imputation algorithms (static or dynamic),then option will allow you to realize all your imputation tasks by saving a database without any missingvalues. Indeed, each missing value is replaced by taking into account its conditional probability distri-bution, returned by the Bayesian network, given all the known values of the line. If the database containsdata for test and data for learning, the user can choose which kind of data he wants to save: onlylearning data, only test data or the whole data. It is also possible to save only the data correspondingto the selected nodes.

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The states' long name can be saved instead of the states' name.The numerical values in the databaseassociated with the continuous nodes can be saved if they exist. If there is no numerical values asso-ciated with the database and if the option is checked, the numerical values will be created by randomlygenerating a value in each concerned interval. If the database contains weights, they will be savedas the first column in the output file.

• Imputation: Allows the imputation of the missing values of the associated database according to themode selected in the following dialog box:

The data will be saved in the specified file and the long name of the states will be used as specified.If the database contains data for test and data for learning, the user can choose on which kind ofdata he wants to perform imputation: only learning data, only test data or the whole data. The states'long name can be saved instead of the states' name.The numerical values in the database associatedwith the continuous nodes can be saved if they exist. If there is no numerical values associated withthe database and if the option is checked, the numerical values will be created by randomly generatinga value in each concerned interval. However, if there are numerical values in the database, themissing numerical values will be generated from the distribution function of each interval. If the databasecontains weights, they will be saved as the first column in the output file.

• Graphs: Opens the graph editor if a database is associated with the current network.

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2.1. Data Importation Wizard

BayesiaLab allows importing data from:

• text files (CSV, text etc.)

• databases

The data importation is divided into 5 steps:

• Step 1: File (a) or Database (b) visualization

• Step 2: Selection and typing of the variables

• Step 3: Missing value processing and data filtering

• Step 4: Discretization of continuous variables and state aggregation of discrete variables and datatype selection

• Step 5: Import report

Note: for each table in each step, double-clicking on the right side of a column's header will give thepreferred size of each header to each selected column.

Step 1 (a): Data file preview

This wizard allows previewing the file with respect to the specified Field Separator. It allows changingthe file encoding as necessary. When a title line containing the names of the variables exists, thesenames are shown in the column headers; otherwise the variables are automatically named.

This first wizard is also used to specify the strings used to indicate a missing value.

In the same way, it is possible to define filtered values by adding them to the list of filtered values.Each string of this list found in the database will be considered as a filtered value and replaced by *.

• the columns correspond to the variables

• the rows correspond to the samples

However, in Bio-Informatics, and especially in the field of micro-array analysis, the rows correspond tothe variables (e.g. the genes) and the columns correspond to the samples.To deal with this kind of data,one has then to choose the Transpose option.

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In this step, the options allow:

• Specifying separators, i.e. the characters that are used to separate the variables

• Specifying the values which will be considered as missing values

• Specifying the values which will be considered as filtered values for discrete or continuous variables

• Indicating the presence of a title line, i.e. the values of the first line will be used to define the nameof the variables

• Indicating the end line character

• Ignoring the simple and/or double quotes

• Taking into account consecutive separators

It's possible to import only a sample of the data:

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There are three available sampling definitions:

• Random Sample with percentage: a percentage is specified and BayesiaLab randomly selects thecorresponding number of lines from the file.

• Random Sample with size: the number of lines is defined and BayesiaLab randomly selects themin the file.

• Custom Sample: the first and last indices that have to be imported are specified.

It is also possible to specify that a sample of the rows will be used as a test database; the remainingrows will be used as a learning database. You have just to specify in the following dialog box the per-centage of rows to use as test database:

Step 1 (b): Database preview

This wizard allows managing the connectivity with databases. It is divided into 11 parts:

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1. JDBC driver Specification

2. The ... button allows displaying the following wizard for choosing a driver from a list of drivers. Thiswizard indicates:

3.

• the available drivers,

• the syntax of the database URL

• the installation directory.

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4. Database URL. Each driver has its own syntax.When the driver is chosen through the driver selectionwizard, the URL syntax is described.

Note

All the used URLs are saved and available for the next sessions.

5. User: allows specifying the user of the database

6. Password: allows entering the password corresponding to the database user

7. Once the connection is established with the database, this panel lists the available tables of thedatabase. Above, the user can fill the schema and catalog in the two corresponding combo boxes toprecise the tables retrieving (if empty, no filter is applied).The schema and catalog can be filled beforeconnection, or after by clicking on the "Apply" button, to limit the number of available tables proposed.This two combo boxes will be invalidated if the schema or catalog concepts are not part of the targetdatabase.

8. Allows selecting the fields that will be used in the network. An SQL query is automatically generated.

9. Allows entering an SQL query. The button "..." opens the SQL Request dialog:

10. Open: Opens a text file containing a SQL request.•

• Save: saves the edited request into a file.

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• Validate: closes the SQL request dialog and copy the edited request in the data selection panel.

• Cancel: closes the dialog without any change.

11. Allows specifying the number of lines displayed in the windows.

12. Allows entering a string indicating missing values.

13. Allows transposing the data

Note

The left panel lists the available tables in the connected database (limited to 500). However,this help can be impossible to initialize on some database manager. In this case, an errordialog will display and the left panel will invalidate (but you will be connected to the databaseand will be able to send SQL requests in control 8)

Step 2: Selection and typing of the variables

This second wizard is made of three parts:

1. Format: to choose the variables to include in the future Bayesian network and to indicate their type:

• Not distributed: to specify that this column won't be included in the Bayesian network.

• Discrete: each different value of the variable will be considered a state

• Continuous: the values are considered numerical and will be discretized

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• Weight: to consider a numerical column as a weighting variable for the line. Note that there is onlyone weight variable.

• Data type: allows defining which rows will be used for learning of for test. Note that there is onlyone data type variable. The column must contain only two different states.

• Row Identifier: allows defining an identifier for each row. Identifiers can be of any type (string ornumbers) but cannot contain missing values. However, unicity is not required. Two rows can havethe same identifier. These identifiers will be saved with the database and kept in any deriveddatabase (generated by some analysis or tools). This identifier can be used to select a line in thedatabase that will be observed (during Interactive Inference, Interactive Updating or manual selectionon the database). The current identifier is displayed in the status bar.

2. Data View: to view the database and to select variables.Thanks to + it is also possible to selectall the columns and to choose the same processing for all the variables.

3. Information: to get information about the data that will be imported while processing the variables.The statistics Others regroup information about row identifier, weight and data type columns.

Step 3: Missing value processing and data filtering

1. Missing Value Processing: allows specifying, for each variable that have missing values, the kindof processing to apply:

a. Filter: two filters are available

• OR filter: each line that has at least a missing value for one of the variable belonging to the ORrule is discarded

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• AND filter: each line that has missing value for all the variable belonging to the AND rule is dis-carded

b. Replace by: allows specifying the value that will be used to replace the missing values:

• it is possible to set directly the value

• or to use the mean value computed with the available data (continuous variables)

• or to use the modal value computed with the available data (discrete variables)

• or it is possible to choose one of the proposed values in the combo box. These values are theexistent states of the selected column. If several columns are selected, only the common statesare proposed.

c. Infer:

• Static Imputation: the probability distributions of the missing values are estimated based on theavailable data, by considering that all the variables are independent (fully unconnected network).Whereas the previous "Replace by" option allows replacing the missing values with the mostprobable values, the missing values are replaced here by values that are randomly chosen ac-cording to the probability distributions. Even if this decision rule is not optimal at the line level(the optimal rule being the one used by the "Replace by" option), it is however the best rule atthe population level.This imputation process only occurs at the end of the data loading. However,it can also be launched, with respect to the current Bayesian network, by using the Learningmenu, with the Learning the Probabilities menu item.

• Dynamic Imputation: the conditional probability of the missing values is dynamically estimatedbased on the current network and the available data of the line. Each missing value is then re-placed by a value randomly selected with respect to the probability distribution. During learning,a new imputation is realized after each structure modification.This option then brings a rigoroussolution to attack imputation tasks, as it is possible to save the database with all the data pro-cessing results included, i.e. without missing values in that case.

• Structural EM: the probability of each state is dynamically estimated during learning by usingthe current structure and to the available data. These probabilities are directly used for learningthe structure and the parameters, i.e. there is no completion with a specific state.

Dynamic Imputation and Structural EM represent the most rigorous way to process missing values.However, these methods are time costly as they need to carry out inference while learning thestructure of the network. Note also that the choice of one of these methods is applied to all thevariables for which an inference processing has been set. This choice can be changed once thedata are loaded by using the Learning menu. Note that the missing values replacement is dynam-ically taken into account in the information panel.

2. The Data View: a left click on the icon , gives access to statistical information about the distributionof the variable. If a variable has not replaced missing values, then the icon will indicate it in theheader of the column.

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Note

When we want to check or uncheck several states at the same time, you have just toselect the convenient states (by clicking on their names) and to check or uncheck oneof the filters keeping the key pressed in order to do not lose the selection.

Note

The Minimum and Maximum required zones allow creating filters.

It is also possible to use to define filters. Two types of filters are available: OR and AND filters.The filtering system consists in defining the lines that will be imported. If we want to describe the linesthat we want to discard, we have to invert the corresponding logical expression. The example belowdescribes how to filter the smokers that are less than 15 years old. We then have to keep the lineswhere the individual does not smoke OR is older than 15.

Choose the OR filter1

Click2

on Smoker and uncheckTrue

Click3

on Age and specify 15years old in the Requiredminimum field

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Verify the created filter4

Step 4: Discretization of the continuous variables, state aggregation of the discretevariables and data type

If a weight column is specified, it will be used in the different discretization and aggregation algorithms.

If a data type column is specified, the current learning rows will be used in the different discretizationand aggregation algorithms.

Discretization of continuous variables

This last stage occurs when there are continuous variables to take into account into the network.

A manual and four automatic discretization methods are proposed:

• Decision tree : supervised induction of the most informative discretization thresholds with respect toa target variable. The target variable must be discrete, if not it must be manually discretized before.

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• KMeans : data clustering with the KMeans algorithm. The data are standardized. Each obtainedcluster defines an interval.

• Equal distances : design of intervals that have the same width.

• Equal frequencies : design of intervals with the same weight, i.e. containing the same number ofpoints.

• Manual : manual design of intervals using a graphical interface.

The selected discretization method applies for the selected column. If you want to use a unique method(except Manual ) for all the continuous variables, you can click on Select all continuous.

If you want to design your own intervals, the distribution function will then be displayed in the right window(lines are sorted according to the values of the continuous variable; the X-axis represents the numberof individuals and the Y-axis represents the values of the continuous variable). All the manually discretizedvariables can be used as target variable for the decision tree discretization.

The user can switch the view of the data to a representation of the density curve generated by theBatch-Means method. In this view, the data's density curve is displayed.The continuous variable's valuesare represented along X-axis and the density of probability is represented along the Y-axis. The two redareas at each extremity indicate that the curve may not be accurate and can't be used to place heresome discretization points.

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This window is fully interactive and allows, in both view:

• Adding a threshold: Right Click

• Removing a threshold: Right Click on the threshold

• Selecting a threshold: Left Click on a threshold

• Moving a threshold: Left Click down and mouse move, the current Y-Coordinate appears in the Pointbox :

• Zooming: Ctrl + Left Click down + move + release to define the area that we want to enlarge. In thedistribution function, the zoom will be done vertically and in the density curve, it will be done horizontally.It is possible to zoom successively as much as you need.

• Unzooming: Ctrl + Double Left Click

Besides this distribution function, the button: allows having access to the threeautomatic discretization methods through a new dialog. This part can be considered a wizard for themanual discretization as it is possible to launch these methods, to see the resulting discretization on thedistribution function, and then to modify the result by moving, deleting and adding thresholds.

If the chosen discretization fails, a dialog box is displayed to warn the user. In this dialog it can changethe chosen discretization.

It is also possible to transfer the defined discretization points to other variables. The button: allows getting the list of the continuous variables. Simply select from that list the

variables to process.

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Note

The transfer applies only if the variation field of the selected variables is compatible withthe variation field of the original variable.

NB: If a filtered value is defined for a continuous variable, a filtered state will be created at the endof import as a new interval.This interval will be added following the intervals defined by the discretization.The name of the state associated with the interval is * by default.

State aggregation of a discrete variable

It is possible to aggregate the states of a discrete variable into one new state. This processing has tobe carried out for the discrete variables that have too many states. When a discrete variable is selected(left click on the corresponding column), the following window appears

It allows:

• Creating an aggregate: The list of states appears in the Aggregation zone. To make a selection,click on the chosen state and maintain pressed for a partial selection or maintain pressed fora multiple selection. Once the selection done, click on , the new aggregate appears in theAggregates list.

• Modifying an aggregate: The selection of an aggregate allows adding new states.

• Renaming an aggregate: The name edition is available thanks to a double-click on it

• Removing an aggregate:You can remove an aggregate by selecting it and pressing

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Besides this a priori aggregation process, it is also possible to use the correlation of the variable with atarget variable which can be discrete or continuous but manually discretized before. By check-ing and selecting a target variable, BayesiaLab displays the conditional probability table ofthe target variable knowing the current variable.

In this screen capture, the probability distribution of the target node (Cancer) is displayed with respectto each state of the current variable. For binary or "binarized" (a target state has been set) target variables,the column "Correlation" is used to highlight the difference between the conditional probability of thefirst target state and its marginal probability. Green bars (the conditional probability is higher than themarginal one) and red bars (lower) greatly improve the readability of the results. It is then possible toaggregate states that have the same relation with the target just by using the colors.

NB: The exact value of the difference is given in a tooltip when you point to the corresponding bar.

Besides the visual help, it is also possible to have a special aggregation wizard for binary or "binarized"target variables by clicking on

The colored bar represents the variation field of the differences between the conditional and marginalprobabilities of the first target state. This bar is interactive and allows defining aggregation thresholds:

• Adding a threshold: right click,

• Modifying a threshold: left click down and mouse move on the deltas-axis, or by selecting thethreshold value from the list and by directly editing it thanks to a double left click.

• Removing a threshold: right click on the threshold.

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Defining just one threshold equal to 0 allows grouping all the "green" and "red" states automatically.

The button: displays a new dialog that allows detecting automatically how to groupthe states. This algorithm uses a decision tree to find what the best threshold is in order to create thegiven number of aggregates.

Once the wanted final state number chosen, the found best thresholds are displayed in the table andyou can click on the OK button to apply the new generated aggregates.

NB: If a filtered value is defined for a discrete variable, a filtered state will be created with * as nameby default. This state could not be aggregate with the other states.

State aggregation of several discrete variables

It is possible to automatically perform the aggregation of the states of several discrete variables by se-lecting several discrete columns in the table or by clicking on the button Select all discrete. It bringsup a new panel:

It allows performing automatic aggregation like in the Automatic Aggregation Wizard over the selectedvariables that the initial state number is greater or equals to the specified number. You have simply tospecify the target node and the state and indicate how many states you want at the maximum. If thetarget node is one of the selected variables, it will remain unmodified.

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Sometimes, the algorithm cannot find any grouping because the current variable and the specified targetare independent. In this case, the unmodified variables will be displayed in a dialog at the end of theautomatic aggregation process.

It is possible to stop the process by clicking on the close button of the progress bar. The already treatedvariable will be conserved and the other will stay as before.

Data type

If a column if a used as data type, you can configure select which state you want to use for learning andfor test. To do this, use the corresponding combo boxes to change the type associated to each state.

Import Report

After a successful database import, it is possible to display the HTML import report.

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The first column displays the names of the imported variables. The second column displays the typeassociated with each variable.The third column shows the different states of each variable if necessary.Information contained into the last column may vary according to the type of the variable:

• Data Type: indicates, for each state, if this state will be used for learning or test and how many theyare in the database.

• Weight: no necessary information.

• Discrete: indicates, for each state, the possible aggregated states that were aggregated. The colorof the last cell indicates if the states of the node were really aggregated.

• Continuous: indicates, for each state, the intervals limits. After that, the asked discretization and thereally obtained discretization are shown.The background of this cell is colored according to the obtaineddiscretization to allow a quick identification.

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2.2. Data Association Wizard

BayesiaLab allows associating data from:

• text files (CSV, text etc.)

• databases

The data association is divided into 6 steps:

• Step 1: File (a) or Database (b) visualization (see Step 1 in Data Importation Wizard)

• Step 2: Selection and typing of the variables (see Step 2 in Data Importation Wizard)

• Step 3: Missing value processing and data filtering (see Step 3 in Data Importation Wizard)

• Step 4: Node and state associations

• Step 5 (if necessary): Discretization of continuous variables and state aggregation of discrete variables(see Step 4 in Data Importation Wizard)

• Step 6: Association report

Note: for each table in each step, double-clicking on the right side of a column's header will give thepreferred size of each header to each selected column.

Step 1 (a): Data file preview

Same as Step 1(a) in Data Importation Wizard.

Step 1 (b): Database preview

Same as Step 1(b) in Data Importation Wizard.

Step 2: Selection and typing of the variables

Same as Step 2 in Data Importation Wizard.

The type of each column is detected automatically from the type of the nodes if it is possible.

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The button Unmatched Columns displays all the columns in the database that are not in the network.The following dialog is displayed and allows the user to distribute or not the selected columns:

Step 3: Missing value processing and data filtering


Step 4: Node and state associations

This step is used to link the columns in the database to the nodes of the network It is dependent of thethree previous steps and specially the selection of the variables' type.

There are three available associations:

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• Discrete column - Discrete node

• Discrete column - Continuous node

• Continuous column - Continuous node

If it is possible, the valid associations are detected automatically the first time the panel is displayed.

The zone 1 contains the list of the variables contained in the database and not already associated to anode of the network or added as a new node of the network. As you can see, the variable GeographicZone contained in the database is discrete and has no corresponding node in the network. If you wantto add it as a new node, simply select it and click on the button , otherwise, if you don't want toadd it, do nothing. You can process in the same way for the continuous node N. You can also selectand add several nodes at the same time.

The zone 2 contains the list of the nodes contained in the network and not already associated to acolumn of the database. If you want to link a variable from the database to a node of the network, simplyselect each one and press the button . All remaining nodes in this list will not be linked to a columnof the database and will be considered as hidden node in the network.

The zone 3 contains the buttons used to add or remove associations.

The zone 4 contains the list of associations. It can contain also added variables from the database thatwill be treated as new nodes in the network. A double-click on an association display, if necessary, adialog used to edit a discrete or a continuous association. As you can see, some associations show awarning icon. This icon indicates that some unusual behaviors are present in those associations.

The zone 5 contains a list containing the details of each warning of associations located in zone 4. Ifyou select a warning in the list, the corresponding association will be selected in the zone 4. When themouse hovers on the list, a tooltip shows the content of the warning. A double-click on it opens the

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convenient association editor in order to verify or modify the association. If you want to remove an asso-ciation or an added node, select it in the list and press the button .

The zone 6 contains three buttons. The first and second buttons allow extending automatically theminimum and maximum of each continuous node that does not fit the database's limits.The third buttonallows filtering automatically each row that does not fit the network's limits.

Discrete column association

When you want to add or edit an association between a discrete column of the database and a discreteor continuous node, a dialog box appears:

The zone 1 contains the list of the states from the database that are not already linked to a state of thenode or directly added as a new state.To perform an association, select a state in the zone1 and a statein the zone 2 and press . If you want to add a state without linking it to a state of the node, simplyselect it and press the button .

The zone 2 contains the list of the states from the node of the network. This list will never be modified.Even if an association is done, the corresponding state of this list will not be removed and can be reusedfor another association. It allows linking several states from the database to the same state of the nodefrom the network. To perform an association, select a state in the zone1 and a state in the zone 2 andpress . The state from the zone 1 will be removed and the association will be added in the zone4.

The zone 3 contains the buttons to add or remove states' associations.

The zone 4 contains all the associated and added states. An association can be removed by selectingit in the list and pressing the button .

After association, the dialog looks like:

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If there are still some states not linked in the zone1, these states will be removed from the database.

By default, the database's states which are the same as the network's ones, as the aggregates or asthe states' long names will be automatically linked.

NB: If filtered values exist in the database but are not declared in the network, it is possible to mergethem with the specific state *, if it exists. In this case, this state will be automatically defined as filteredfor each concerned node.

Continuous column association

When you want to add or edit an association between a continuous column of the database and acontinuous node, a dialog box appears:

This dialog is displayed only if the limits of the variable from the database are outside the limits of thenode from the network.

By default, the limits of the node of the network are used and all the values outside these limits willbe removed from the database. If you want to keep them, use the corresponding options.

NB: If filtered values exist in the database but are not declared in the network, it is possible to mergethem with the specific state *, if it exists. In this case, this state will be automatically defined as filteredfor each concerned node.

Step 5: Discretization of the continuous variables and state aggregation of thediscrete variables

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This step occurs only when some columns of the database are not linked with nodes of the network butare distributed. These columns will create new nodes in the network and must be discretized if they arecontinuous and their states can be aggregated if they are discrete.


Step 6: Associate Report

After successful data import, it is possible to display the HTML associate report.

This report may contain three tables:

1. The modified nodes table:

• For the discrete nodes, will be indicated, if necessary, the correspondence between the states inthe database and in the network.

• For the continuous nodes, will be indicated, if necessary, the initial minimum of the data and theretained final minimum and also the initial maximum and the retained final maximum.

2. The hidden nodes table: indicates the node that are in the network and that don't have any associateddata.

3. The added nodes table: indicate the list of variables added to the network from the database. Thistable is the same as in the import report.

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2.3. Evidence Scenario File

It is possible to associate an evidence scenario file to a Bayesian network. This file contains a series ofevidence sets that are applied on the Observable Nodes of the network, i.e. the nodes that do not havea cost set to "Not Observable" (see costs). This file can be written by the user and then imported, butit can be also generated by registering the evidences done with the monitors. After that, this generatedfile can be exported. A comment can be associated to each set of evidences. This comment will bedisplayed in the network's status bar during interactive inference or interactive updating.

Kinds of evidences

There are four possible kinds of evidences which are the same as ones obtained with the monitors:

1. Exact evidence on a state of a node

2. Likelihood distribution over the states of a node

3. Probability distribution over the states of a node (fixed distribution with exact inference or computationof the corresponding likelihoods with approximate inference)

4. Target mean for a node (determining a probability distribution corresponding to the target mean andtaking the others observations into account)

Caution

Sometimes a fixed probability distribution cannot be done because the algorithm usedto reach the target distribution fails to converge. In this case the corresponding probabilityfixing is not done and the node comes back to its initial state. An information messageis displayed in the console.

Temporal

When a network is temporal, it uses the Time variable or although it has at least a temporal node, thetime step can be set by indicating its value with a positive or null integer.

Syntax

It is a text file where each line is formatted with the following grammar:

for the temporal networks:

<line> ::= <time step> [<semicolon> [<evidence> | <likelihood> | <probability>| <mean>]]+[<comment>]

<time step> is an integer representing the time step at which the following evidences are set.

for the not temporal networks:

<line> ::= [<evidence> | <likelihood> | <probability> | <mean>] [<semicolon> [<evidence> | <like-lihood> | <probability>| <mean>]]* [<comment>]

<semicolon> is the character ; (semicolon)

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<colon> is the character : (colon)

<evidence> ::= <variable> <colon> <state>

it is possible to use directly a numerical value for a continuous node:

<evidence> ::= <variable> <colon> <numerical value>

<likelihood> ::= <variable> <colon>l{ <likelihood list> [<semicolon> <likelihood list>]+ }

<likelihood list> ::= <state> <colon> <degree of likelihood>

<probability> ::=<variable> <colon> p{ <probability list> [<semicolon> <probability list>]+ }

<probability list> ::= <state> <colon> <degree of probability>

<mean> ::= <variable> <colon> m{ <numerical value> }

<variable> corresponds to the variable name, flanked by question marks, for which there is an evidence,and <state> indicates the concerned state.

<comment> ::=<two slashes> <any character string>

The following example contains exact evidences, likelihoods and probabilities for four time steps:

0;?Valve1?:OK;?Valve2?:OK;?Valve3?:OK //All the valves are working

2;?Valve1 t+1?:l{OK:0.8;RC:0.9;RO:0.9}

20;?Valve2 t+1?:l{OK:0.3;RO:0.3;RC:0.3};?Valve1 t+1?:p{OK:0.2;RO:0.4;RC:0.4}

30;?Valve3 t+1?:OK;?Valve1 t+1?:p{OK:0;RO:0.8;RC:0.2}

When a temporal evidence file is associated to a temporal network, the evidences are taken into accounteach time the time meter reaches one of the specified time steps. When the file and the network are nottemporal, the evidences are taken into account during interactive inference or during interactive updating.

The following example shows not temporal evidences and also evidences with numerical values:

?Smoker?:Yes;?Age?:25.5;?Bronchitis?:p{Yes:0.8;No:0.2}//Young smoker with a large probability

of bronchitis

?Smoker?:No;?Age?:70;Dyspnea:l{Yes:0.8;No:0.5} //Non-smoker senior person

Creating evidences with monitors

When the user is in validating mode, it is possible to store the evidences done on the monitors with thebutton located in the monitor toolbar. When a set of evidence is added, it is possible to append acomment to it thanks to the proposed dialog box.

When an evidence scenario file is created or imported, the icon is displayed in the network's statusbar. The tooltip associated to this icon indicates the number of evidence sets contained in the file. Aclick on this button allows us to remove the association between the network and the file.

Importing/Exporting evidence scenario files

The menu Data>Associate an Evidence Scenario File allows loading a file from the hard drive. Any in-valid evidence is ignored. At the end of the importation, a summary of the errors met is displayed if ne-cessary.

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The menu Data>Export an Evidence Scenario File allows saving, into a text file, the current evidencescenario file.

Batch exploitation

If an evidence scenario file is associated to the network, it is possible to use it as data source for thebatch exploitation of the network:

• Batch labeling

• Batch inference

• Batch labeling with most probable explanation

• Batch inference with most probable explanation

• Batch joint probability

• Batch likelihood

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2.4. Graphs

The graph editor allows displaying six different graphs. The graphs are obtained from the data storedin the database. Some of these graphs cannot be used if there is no continuous node in the network.Moreover, the database must also contain the exact values of the continuous nodes. To do this, youmust check the convenient option in the settings.

If the database contains data for test and data for learning, the user can choose which kind of datahe wants to display: only learning data, only test data or the whole data.

• Bar chart: always available.

• Occurrences matrix: always available.

• Distribution function: always available.

• Scatter of points (2D): only with continuous.

• Colored Line Plot: only with at least one continuous.

• Scatter of points (3D): only with continuous.

• Bubble chart: only with continuous.

2.4.1. Bar chart

The bar chart graph displays the frequencies of a node's discrete states.

Parameters: Select a variable in the combo-box, change the color as you need by clicking on the coloredsquare and then display the graph by pressing on the button.

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Graph: When you move the mouse over the graph, the information in the top panel is updated. It displayson which state the cursor is and how many times the state is in the database.The total number of statesis also indicated.

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2.4.2. Occurrence matrix

The occurrence matrix graph displays a dimension table and the Khi2 test or G test estimating theprobability of independence between the two variables.

The independence test used can be changed thanks to the settings of the statistical tools.

Parameters: Select a variable in each combo-box, check the needed option if you want to display thevalues as absolute, percent, line percent or column percent and then display the graph by pressing onthe button.

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Graph: The right panel contains all the information about the Khi or G independence tests and thecomputed degree of freedom. The missing values are not taken into account in the computation of theindependence test but the weights are.

2.4.3. Distribution function

This graph displays the distribution function of the selected continuous variable.

Parameters: Select a continuous variable in the combo-box and then display the graph by pressing onthe button.

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Graph: The horizontal lines represent the limits of the node's intervals. When you move the mouse overthe graph, the information in the top panel is updated. It displays the coordinates of the cursor in thegraph. The total number of displayed values is also indicated.

You can perform a zoom on the graph by pressing the left button, drag the mouse and then releasingthe button: the selected area will be magnified. To remove the zoom, double-click on the graph, thedefault view will be restored.

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2.4.4. Scatter of points (2D)

This graph displays the scatter plot of the two selected variables.

Parameters: Select a continuous variable in each combo-box. You can change the point size with theconvenient slider. The point jittering slider allows adding a random noise to the position of each point toavoid overlapping when many of the coordinates are the same (for example with integer coordinates).The jittering is identical whatever the zoom.

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Graph: The black lines represent the limits of the nodes' intervals. When you move the mouse over thegraph, the information in the top panel is updated. It displays the coordinates of the cursor in the graph.The total number of displayed values is also indicated. If you click inside a point (or several if the pointsoverlap), a dialog appears containing the rows of the database corresponding the selected points.


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2.4.5. Colored Line Plot

This graph displays the colored line plot of the two selected variables.The continuous variable is displayedalong y-axis. The indices of the values in the database are along x-axis. The color variable gives thecolor of the curve for each index.

Parameters: Select a continuous variable in the first combo-box and a variable for the color in thesecond combo-box.

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Graph: The black lines represent the limits of the vertical node's intervals. When you move the mouseover the graph, the information in the top panel is updated. It displays the coordinates of the cursor inthe graph. The total number of displayed values is also indicated. If you click inside a point (or severalif the points overlap), a dialog appears containing the rows of the database corresponding the selectedpoints.


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2.4.6. Scatter of points (3D)

This graph displays the scatter plot of the two selected continuous variables. The color of each pointrepresents a state of the third node.

Parameters: Select a continuous variable in the first two combo-boxes. The states of the third variablewill be represented by different colors. You can change the point size with the convenient slider. Thepoint jittering slider allows adding a random noise to the position of each point to avoid overlapping whenmany of the coordinates are the same (for example with integer coordinates). The jittering is identicalwhatever the zoom.

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Graph: The black lines represent the limits of the nodes' intervals. When you move the mouse over thegraph, the information in the top panel is updated. It displays the coordinates of the cursor in the graph.The total number of displayed values is also indicated. If you click inside a point (or several if the pointsoverlap), a dialog appears containing the rows of the database corresponding the selected points.


The right panel displays the color associated with each state of the third variable.You can modify directlythe colors by clicking on each colored square.

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2.4.7. Bubble chart

This graph displays the bubble chart of the three selected continuous variables. The size of the bubblesrepresents the values of the third node.

Parameters: Select a continuous variable in each combo-box. You can change the maximum bubblesize with the convenient slider. The point jittering slider allows adding a random noise to the position ofeach bubble to avoid overlapping when many of the coordinates are the same (for example with integercoordinates). The jittering is identical whatever the zoom.

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Graph: The black lines represent the limits of the nodes' intervals. When you move the mouse over thegraph, the information in the top panel is updated. It displays the coordinates of the cursor in the graph.The total number of displayed values is also indicated. If you click inside a bubble (or several if thebubbles overlap), a dialog appears containing the rows of the database corresponding the selectedbubbles.


The right panel displays the color of the bubbles.You can change it by clicking on it.

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3. Edit

• Undo: (modeling mode)

• Redo: (modeling mode)

• Select All: Select nodes and arcs.

• Select Nodes

• All: Select all the nodes.

• Discrete: Select the discrete nodes.

• Continuous: Select the continuous nodes.

• Constraint: Select the constraint nodes.

• Decision: Select the decision nodes.

• Utility: Select the utility nodes.

• Excluded: Select the excluded nodes.

• Disconnected: Select the disconnected nodes.

• Missing Values: Select the nodes having a percentage of missing values greater than a giventhreshold:

• Assessments: Select allt the nodes having at least one assessment in their conditional probabilitytables.

• Select Arcs

• All: Select all the arcs.

• Fixed: Select the fixed arcs.

• Temporal: Select the temporal arcs.

• Not Oriented: Select the not oriented arcs.

• Invert All Selection: Select the arcs and the nodes that are not selected and unselect the others.

• Invert Selection

• Nodes: Select the nodes that are not selected and unselect the others.

• Arcs: Select the arcs that are not selected and unselect the others.

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• Delete Selection (modeling mode): Delete the selected nodes and arcs.

• Delete (modeling mode):

• All Arcs: Delete all arcs.

• Unfixed Arcs: Delete all unfixed arcs.

• Disconnected Nodes: Delete all nodes that are disconnected.

• Virtually Disconnected Nodes (KL Force): Delete all virtually disconnected nodes only if the Arcforce analysis has occurred and the Arc force trim has been used in the validation mode:

• Edit Structural Coefficient (any mode): opens a dialog box in order to change the structuralcoefficient from 0 to 150. The default value is 1.

• Edit Costs (any mode): opens the dialog box that allows associating a cost with the observation ofa variable (see Cost management).

• Edit Classes (any mode): opens the dialog box that allows the creation and the edition of theclasses associated with the nodes (see Classes management).

• Edit Constants (modeling mode): opens the dialog box that allows the creation and the edition ofthe constants that will be used in the formulas describing the probability distributions of the nodes(see Constants management).

• Edit the Forbidden Arcs (modeling mode): opens the dialog box that allows the creation of forbiddenarcs in the network's structure (see Forbidden arcs management).

• Edit the Temporal Indices (modeling mode): opens the dialog box that allows editing the temporalindices associated to the nodes of the network (see Temporal indices).

• Edit State Virtual Numbers (modeling mode): opens the dialog box that allows editing the statevirtual numbers associated to nodes and used for learning.

• Edit Local Structural Coefficients (modeling mode): opens the dialog box that allows editing thelocal structural coefficients of each node. This coefficient is used for structural learning.

• Edit Experts (modeling mode): opens the dialog box that allows editing the experts of the network.Experts are used for assessment sessions.

• Use Time Variable (modeling mode): allows using the parameter variable that represents the timein the equations.

• Cut: Cut the selected nodes and put them in the clipboard.

• Copy: Copy the selected nodes in the clipboard.

• Paste: Paste the nodes that are in the clipboard (a right click before pasting allows specifying thedestination).

• Search: Search for nodes, arcs and edges by the names of the nodes and/or the classes.

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4. View

• Modeling Mode: mode where the graph visualization panel is visible and where actions ofmodeling and learning are carried out.

• Validation Mode: mode where the graph visualization panel and the monitor visualizationpanel are visible and where actions of validation and exploitation of the networks are carried out.

• Automatic Positioning: uses original algorithms to try to layout the network as well as possible. Aslider is added to the tool bar to set the arc length.

1. The symmetric algorithm uses repulsive and attractive forces to define the graph layout. It's a veryeffective algorithm that returns good graph layouts for moderately connected graphs.

The Settings allows modifying the parameters of this algorithm.

2. The Dynamic algorithm is particularly efficient with weakly connected networks. The goal of thisalgorithm is to try to:

• set the parents above their children,

• avoid crossing arcs,

• set the arc length proportional its force (the stronger the probabilistic relation represented by thearc is, the shorter the arc is) when the automatic positioning is launched within the Validationmode jointly with the Arc Analysis option active.

3. The Genetic Algorithm is useful for highly connected networks. This algorithm takes into accountan evaluation function that is based on:

• the relationship between the nodes (the parents try to get a position above their children),

• the verticality of the arcs

• the overlapping of the nodes

• the force of the arcs when the automatic positioning is launched within the Validation modejointly with the Arc Analysis option active;

• the intersection of the arcs with other arcs and with the nodes.

The Settings allows to weight the evaluation function parameters and to change those correspondingto the genetic algorithm.

4. The Mutual information mapping is only available for fully unconnected networks with an associateddatabase. This layouting algorithm computes the mutual information matrix and then uses the ge-netic algorithm to try to find a global node mapping where the proximity of two nodes is inverselyproportional to their mutual information.

The Settings allows weighting the genetic algorithm parameters.

5. The Random positioning allows setting a random position to each node.

• Zoom: zooming the nodes

• Zoom in: increase the size of the network. If a node or a group of nodes is selected, the selectionwill be centered in the window (if possible).

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• Zoom out: decrease the size of the network. If a node or a group of nodes is selected, the selec-tion will be centered in the window (if possible).

• Default zoom: go back to the default zoom level. If a node or a group of nodes is selected, theselection will be centered in the window (if possible).

• Best fit: move and adjust the size of the network in order to fit the window. If a node or a groupof nodes is selected, the selection will fit the window.

• Center: center the network in the window.

• Horizontal mirror: perform a horizontal inversion of the positions of the nodes.

• Vertical mirror: perform a vertical inversion of the positions of the nodes.

• Top left corner: move the graph in the top left corner of the window.

• Hide Node Names: the name of the nodes is no more displayed under them.

• Hide information: hide comment indicators of nodes and arcs as well as the missing values,filtered state and error indicators of each node.

• Display node comments: display the comment of the nodes over them.

• Display arc comments: display the comment of the arcs over them.

• Display node tags: display the color tags of the nodes.

• Display arc tags: display the color tags of the arcs.

• Display the node's image: display the image associated to a node instead of its default represent-ation.

• Display grid: display the positioning grid. The spacing can be modified through the display pref-erences.

• Display the network's skeleton: hide the head of the arcs in the network in order to avoid invalidcausal interpretation with the direction of the arcs. Only in Validation mode.

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5. Learning

This menu gives access to different learning algorithms.

• Missing value processing: allows to choose the missing value processing algorithm

• Static completion

• Dynamic completion

• Structural EM

• Stratification : when the target value has a very weak representation (as usually the fraud for example),stratification allows modifying the probability distribution of the target variable (by using the internalweights associated to the states). This modification of the probability distribution can then permit tolearn a network that is structurally more complex. Once the structure learned, the parameters (i.e. theprobability tables) are estimated on the unstratified data.

In the following dialog box, you can indicate the proportion of each state of the specified node youwant to obtain. The initial value corresponds to the proportion of the database. You have simply tomove the slider or edit directly the value for each state.

When stratification is done, the icon is displayed in the status bar. It is possible to remove thestratification by right-clicking on this icon to display the contextual menu and to choose to remove thestratification.

• Estimation of the probabilities: allows updating the probabilities tables by using the frequencies ofthe cases that are observed in the database, smoothed or not depending on the user choice definedby the settings. If the database contains missing values, this algorithm also launches the missingvalue processing. At the end of the estimation, the score of the Bayesian network (structure and newprobabilities), is displayed in the console and automatically inserted in the network's comment.

• Structural learning of Bayesian networks: a broad set of learning algorithms is proposed to be ableto solve any kind of Data Mining tasks:

• unsupervised learning for discovering all the probabilistic relations in the data,

• supervised and semi-supervised learning for the characterization of a particular variable,

• unsupervised learning to invent new concepts.

If the current Bayesian network has existing arcs, a dialog box appears to indicate if this Bayesiannetwork corresponds to an a priori knowledge that the learning algorithms have to take into account.

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In that case, an equivalent number has to be specified to indicate how many cases have been usedfor the construction of that network (by learning or expertise). This number is automatically set whenthe network is learned from a database. It corresponds to the sum of the weights of the database'slearning set if weights are associated, or to the number of examples in the learning set. A virtualdatabase representing that knowledge is then added to the current database in order to take into ac-count this a priori knowledge. A new icon is then added in the task bar:

All the learning algorithms that are in BayesiaLab are based on the minimization of the MDL score(Minimum Description Length). This score takes into account both the adequacy of the Bayesiannetwork to the data, and the structural complexity of the graph. The score values are available in theconsole during learning. The score of a given network can always be computed by updating itsprobabilities.

The excluded nodes are not taken into account in the learning algorithms.

The filtered states are taken into account.

A compression rate is available in the console.This indicator measures the data compression obtainedby the network with respect to the previous network (usually, the unconnected network). This rate,which corresponds to the part "adequacy of the network to the data" of the MDL score, then not onlygives an indication on the probabilistic links that are in the network, but also the strength of theselinks. For example, with a database containing two binary variables that are strictly identical, the cor-responding network will link these variables and describe in the conditional probability table that thevalue of the second variable is deterministically defined by the first variable. The compression ratewill be then equal to 50%.

• learning policies: if the network has Decision and Utility nodes, action policies can be learned forstatic Bayesian networks and for Dynamic Bayesian networks. The scheme used for policylearning relies on dynamic programming and reinforcement learning principles, which makes thislearning available with exact as well as approximate inference. Learning policies is only available inValidation mode.

5.1. Association Discovering

Set of algorithms allowing unsupervised learning to discover all the probabilistic relations in the data

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The number of Bayesian networks that can be designed for a given number of variables is so great thatit is impossible (except in extreme cases) to carry out an exhaustive search of the best network. Thelearning algorithms rely then on a set of heuristics that allows reducing the search space. BayesiaLabcomes with four structural learning algorithms (discovering of the network structure and estimation ofthe corresponding conditional probability tables) that are conceptually different, from the faster to theslower.The heuristics that are used being different, the results of each method can be different. However,as each learning methods uses the same metric (the MDL score), the resulting networks can be easilycompared. The score is available in the console and is also automatically inserted in the commentassociated with the network. The lower the score is, the better the network is.

For each learning algorithm there are startup options indicating that all arcs will be deleted beforelearning and allowing the user to define a Structure Equivalente Example Number, i.e. a virtualdatabase with the indicated size representing the current sructure:

Maximum spanning tree

This learning algorithm is by far the quickest unsupervised learning algorithm. Indeed, it relies only ontwo passes. The first one consists in computing the a priori weight of all the binary relations between allthe variables, the second one consists then in constructing the maximum weight spanning tree withthose relations. Even if the resulting network is not optimal, it can then be used for a first imputation ofthe missing values, it can be used as the initial network before using Taboo or EQ, and it can also beused for the variable clustering with there is a lot of variables.

The user can choose between two different scoring methods for this learning: the Minimum DescriptionLength and the Pearson's Correlation.

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However, arcs that are fixed (the blue ones) are treated as normal arcs but the forbidden arcs aretaken into account. The temporal indices are also taken into account.

At the end of the learning, a tree without oriented arcs is obtained. To obtain a Bayesian network, thearcs will be oriented so as to avoid introducing V-structures. However, the use of fixed arcs can introduceV-structures.

Taboo

Structural learning implementing the Taboo search in the space of the Bayesian networks. This methodis particularly useful for refining a network built by human experts or for updating a network learned ona different data set. Indeed, beyond taking into account the a priori knowledge represented by a networkand an equivalent number of cases, the starting point of Taboo is the current network (and not thefully unconnected network (no arc), as this is the case for SopLEQ and Taboo Order). Furthermore, arcsthat are fixed (the blue one) remain unchanged and the forbidden arcs are taken in account. Thetemporal indices are also taken into account.

It is possible to define the size of the taboo list as well as the maximum numbers of parents and childrenallowed. If these options are not checked, they are not taken into account.

In addition to standard options, it is possible to maintain the current structure of the network to startlearning.

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EQ

Search method looking for the equivalence classes of Bayesian networks. This method is very efficientbecause it allows avoiding a lot of local minima and to strongly reduce the size of the search space. Asthe Taboo algorithm does, EQ can start with the current network. Furthermore, the fixed arcs are treatedas normal arcs and the forbidden arcs are taken into account. The temporal indices are also takeninto account.

In addition to standard options, it is possible to maintain the current structure of the network to startlearning.

Here is a scientific reference about this learning method:

P. Munteanu, M. Bendou, The EQ Framework for Learning Equivalence Classes of Bayesian Networks,First IEEE International Conference on Data Mining (IEEE ICDM), San Jos , novembre 2001.

SopLEQ

Search method based on a global characterization of data and on the exploitation of the equivalenceproperties of Bayesian networks. Arcs that are fixed (the blue ones) are treated as normal arcs but theforbidden arcs are taken into account. The temporal indices are also taken into account.

Here are some scientific references about this learning method (sorry, but the direct reference is inFrench):

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L. Jouffe, Nouvelle classe de méthodes d'apprentissage de réseaux bayésiens, Journées francophonesd'Extraction et de Gestion des Connaissances (EGC), Montpellier, janvier 2002 P. Munteanu, M. Bendou,The EQ Framework for Learning Equivalence Classes of Bayesian Networks, First IEEE InternationalConference on Data Mining (IEEE ICDM), San José, novembre 2001. L. Jouffe, P. Munteanu, NewSearch Strategies for Learning Bayesian Networks, Proceedings of Tenth International Symposium onApplied Stochastic Models, Data Analysis, Compiègne, juin 2001.

Taboo Order

Learning method using Taboo search in the space of the order of the Bayesian network nodes. Indeed,finding the best Bayesian network for a fixed node order is an easy task that only consists in choosingthe parents of a node among the nodes that appear before it in the considered order. This is the morecomplete search method, but also the more time consuming. Arcs that are fixed (the blue ones) aretreated as normal arcs but the forbidden arcs are taken into account. The temporal indices are alsotaken into account.

In addition to standard options, it is possible to define the size of the taboo list for Taboo Order.

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5.2. Characterization of the target node

Set of algorithms allowing the learning of Bayesian networks that have a structure entirely dedicated tothe characterization of a target variable.

For each learning algorithm there are startup options indicating that all arcs will be deleted beforelearning and allowing the user to define a Structure Equivalente Example Number, i.e. a virtualdatabase with the indicated size representing the current sructure:

• Naive Bayes: Bayesian network with a predefined architecture in which the target node is the parentof all the other nodes.This structure thus states that the target node is the cause of all the other nodesand that the knowledge of its value makes each node independent of the others. In spite of thesestrong assumptions, which are false in the majority of the cases, the low number of probabilities toestimate makes this structure very robust, with a very short learning time as only the probabilitieshave to be estimated.

• Augmented Naive Bayes: partially predefined structure allowing relaxing the strong constraint ofconditional independence mentioned above. This architecture is made up of a naive architecture,enriched by the relations between the child nodes knowing the value of the target node (the commonparent).The prediction accuracy of this algorithm is better than those obtained by the naive architecture,but the unsupervised search of the child relationships can be time consuming.

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• Tree Augmented Naive Bayes: partially predefined structure allowing relaxing the strong constraintof conditional independence mentioned above. This architecture is made up of a naive architectureon which a maximum spanning tree is learned. The prediction accuracy of this algorithm is betterthan those obtained by the naive architecture, but not as good as obtained with Augmented NaiveBayes; however, this algorithm is much quicker than it.

• Sons & Spouses: structure in which the target node is the parent of a subset of nodes having poten-tially other parents (spouses). This structure is to some extent an augmented naive architecture inwhich the children set is not fixed a priori, but searched according to the marginal dependence of thenodes on the target. This algorithm thus has the advantage of highlighting the nodes that are notcorrelated to the target. The learning duration is comparable with the augmented naive architectureone.

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• Markov Blanket Learning : algorithm that searches the nodes belonging to the Markov Blanket ofthe target node, i.e. fathers, sons and spouses. The knowledge of the values of each node of thissubset of nodes makes the target node independent of the all the other nodes. The search of thisstructure, which is entirely focused on the target node, makes it possible to obtain the subset of thenodes that are really usefulmuch more quickly than the two previous algorithms. Furthermore, thismethod is a very powerful selection algorithm and is the ideal tool for the analysis of a variable: arestricted number of connected nodes, different kinds of probabilistic relations:

• fathers: nodes that bring more information jointly than alone;

• sons: nodes having a direct probabilistic dependence with the target;

• spouses: nodes those are marginally independent of the target but which become informative whenknowing the value of the son.

• Augmented Markov Blanket Learning: algorithm that is initialized with the Markov Blanket structureand that uses an unsupervised search to find the probabilistic relations that hold between each variablebelonging to this Markov Blanket. This unsupervised search implies additional time cost but allowshaving better prediction results compared to the first version.

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• Minimal Augmented Markov Blanket Learning : the selection of the variables that is realized withthe Markov Blanket learning algorithm is based on a heuristic search. The set of the selected nodescan then be non minimal, especially when there are various influence paths between the nodes andthe target. In that case, the target analysis result takes into account too much nodes. By applying anunsupervised learning algorithm on the set of the selected nodes, the Minimal Augmented MarketBlanket learning allows reducing this set of nodes, and it results then in a more accurate target ana-lysis.

However, if the task is a pure prediction task (as for example a scoring function), the AugmentedMarkov Blanket algorithm is usually more accurate than its Minimal version since it uses more "piecesof evidences".

• Semi-Supervised Learning :

unsupervised learning algorithm that searches the relationships between the nodes that belong to apredefined distance of the target. This distance is computed by using the Markov Blanket learningalgorithm. The semi-supervised learning algorithm allows learning a network fragment centered onthe target variable. This algorithm is very useful for tasks that involve a lot of nodes, as for examplein micro-arrays analysis (thousand of genes), and for prediction tasks where the Markov Blanket nodeshave missing values, as these nodes do not allow to separate the target node from the other nodesanymore.

In addition to the standard options, the interface allows defining the search depth from the target node:

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5.3. Clustering

This menu gives access to algorithms that allow clustering data in an unsupervised way, in order to findpartitions of homogeneous elements. These algorithms are based on a naive architecture in whichnode CLUSTERS, which is used to model the partitions, is the parent of all the other variables. Unlikesupervised learning, the values of node CLUSTERS are never observed in a database. All these al-gorithms then rely on Expectation-Maximization methods for the estimation of these missing values.

• Output:

• It is possible to create cluster with ordered numerical states. These values are the mean of thescore of each connected node for each state of the cluster node. This score is weighted by thebinary mutual information of each node in order to be more representative of the relationships.If two of these values are strictly identical, an epsilon is added to one of them to obtain two differentvalues.The excluded nodes are not taken into account for the computation of the numerical values.

• Clustering Settings: The assistant gives access to the different search methods:

• Fixed Class Number: the algorithm tries to segment data according to a given number of classes(ranging from 2 to 127). However, it is possible to obtain less clusters than desired;

• Automatic Selection of the Class Number: a random walk is used to find the optimal number ofclasses, starting with the specified number of clusters and increasing that number until obtainingempty or unstable clusters, or reaching the specified maximum number of clusters. The randomwalk is guided by the results obtained at each step;

• Options:

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Sample Size: the sample size option makes it possible to search for the optimal number of classeson data subsets to improve the convergence speed (a sampling by step/trial).The partition obtaining

•

the best score is then used as the initial partition for the search on the entire data set. It is possibleto indicate either a percentage or the exact number of lines to use.

• Steps Number: the number of steps for the random walk. Knowing that it is possible to stop thesearch by clicking on the red light of the status bar while preserving the best clustering, this numbercan be exaggeratedly great.

• Maximum Drift: indicates the maximum difference between the clusters probabilities during learningand those obtained after missing value completion, i.e. between the theoretical distribution duringlearning and the effective distribution after imputation over the learning data set.

• Minimum Cluster Purity in Percentage: defines the minimum allowed purity for a cluster to bekept.

• Minimum Cluster Size in Percentage: defines the minimum allowed size for a cluster to be kept.

• Edit Node Weights: A button displays a dialog box in order to edit weights associated to each variable.

Those weights, with default value 1, are associated with the variables and permit to guide the clustering.A weight greater than 1 will imply that the variable will be more taken into account during the clustering.A zero weight will make the variable purely illustrative.

At the end of clustering, an algorithm allows finding automatically if one of the Clusters node's statesis a filtered state or not. If so, this state is marked as filtered.

At the end of the segmentation, an automatic analysis of the obtained segmentation is carried out andreturns a textual report.This report is a Target Report Analysis, but contains some additional information.It is made of:

• A summary of the learning characteristics (method and parameters, best number of clusters, scoreand time to find the solution);

• A sorted list of the obtained results (number of clusters and corresponding score);

• A list of the clusters sorted according to the marginal probabilities of each cluster (cf. Target ReportAnalysis) ;

• A list of the clusters sorted according to the number of examples really associated to each clusterwhen using a decision rule based on the maximum likelihood for each case described in the learningset;

• A list of the clusters sorted according to the purity of each cluster.The purity corresponds to the meanof the cluster probability computed from each associated example of the learning set. This list alsocomes with the neighborhood of each cluster. The neighborhood of a cluster is the set of clusters thathave a non zero probability during the association of an example to that cluster;

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• A list of the nodes sorted according to the quantity of information brought to the knowledge of theCluster node (cf. Target Report Analysis);

• The probabilistic profile of each cluster (cf. Target Report Analysis).

The Mapping button of the report window allows displaying a graphical representation of the createdclusters:

This graph displays three properties of the found clusters:

• the color represents the purity of the clusters: the more a cluster is blue, the more it is pure

• the size represents the prior probability of the cluster

• the distance between two clusters represents the mean neighborhood of the clusters

The rotation buttons at the bottom right allow rotating the entire graph.

Note

In order to ease the understanding of the obtained clusters, and if at least one variable usedin the clustering has numerical values associated to its states, the states of the node Clusterwill have long names automatically associated. This name will contain the mean value ofall the clustered variables obtained when observing the state of the Cluster.

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5.4. KMeans Clustering

This menu allows clustering data in an unsupervised way thanks to the k-means clustering algorithm,in order to find partitions of homogeneous elements. Originally used only on real variables, this al-gorithm is extended to use also discrete variables. Before running the k-means clustering, the user mustselect the variables on which he wants to apply the algorithm. These variables can be either continuousor discrete but not hidden (i.e. without associated data). Once selected, the clustering tries to regroupthe data into a chosen number of clusters in which each observation belongs to the cluster with thenearest mean. It is similar to the expectation-maximization algorithm for mixtures of Gaussians in thatthey both attempt to find the centers of natural clusters in the data as well as in the iterative refinementapproach employed by both algorithms.

The values of the selected nodes used by the clustering algorithm are computed as following:

1. If the node is continuous and there are continuous values in the database associated to this node,these continuous values are used.

2. If the node has values associated to its states, these values are used.

3. If the node is continuous, the center of each interval is used.

4. If the node is discrete with integer or real states, the values of the states are used.

5. And, if none of the previous cases is valid, integer values are given to each state starting from 0.

In all cases, the filtered values are skipped and the data are standardized.

If there are missing values in the database for the selected variables, the corresponding rows are skippedand not used for the clustering. The weights associated to the chosen rows are taken into account.

Once finished, a node Clusters is created with each state corresponding to each cluster found by thealgorithm.

The data corresponding to the created node Clusters are added in the database. A missing value isput for the node in each row containing missing values for the selected variables.

The following dialog box allows entering the wanted number of clusters. Of course this number must besuperior or equal to 2:

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5.5. Multiple clustering

This tool allows carrying out data clustering on various subsets of variables of the same Bayesiannetwork. The subsets are defined by the classes that are named [Factor_i]. The variables of eachclass [Factor_i] are then used to induce a new variable (the latent variable, i.e. without any correspondingdata in the file) that summarizes them.

Even if it is possible to manually define these classes, they can be created automatically by the variableclustering tool.

A Bayesian network is created for each of these classes.This network contains the variables that belongto the class and the synthetic variable Cluster named [Factor_i]. This variable is added to the corres-ponding class [Factor_i]. It is set as not observable. If the initial network contains fixed arcs, they willbe added to each new Bayesian network if they are included in it, i.e. the extremities of each arc arecontained in the network. At the end of the last data clustering, a final Bayesian network is created. Itcontains all the Clusters and comes with an internal database where all the values of these latent variableshave been inferred with respect to their corresponding network. It is also possible to add to that finalBayesian network the initial variables (the manifest variables).

You must note that the sets containing only one node are not taken in account for data clustering.

The following dialog box allows entering the different parameters for multiple clustering. It naturally reusesmost of the parameters used for data clustering.

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In the Output area, the wizard allows selecting the directory where the various generated networks willbe saved (a network by class [Factor_i] and the final network with all the latent variables). The interme-diate and final databases are saved with the generated networks. The continuous values can be savedwith the databases.This wizard also allows us to add or not all the nodes of the initial network to the finalone. It is also possible to display or not the intermediate report generated for each intermediate network.However, the intermediate reports will always be saved in the target directory.

It is possible to create, for each network, a cluster node with ordered numerical states. These valuesare the mean of the score of each connected node for each state of the cluster node. If two of thesevalues are strictly identical, an epsilon is added to one of them to obtain two different values.

As in data clustering, the number of values of the latent variables can be a priori fixed or found by arandom walk. It can also be defined as being equal to the average number of values of the variablesbelonging to [Factor_i]. The remainder is strictly identical to data clustering.

At the end of each clustering, an algorithm allows finding automatically if one of the [Factor_i] node'sstates is a filtered state or not. If so, this state is marked as filtered.

At the end of each clustering, an automatic analysis of the obtained Bayesian network is carried out anda target analysis report is generated. This report is identical to the one generated by data clustering.It can be displayed if the convenient option has been selected. However, it is always saved in the targetdirectory.

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At the end of the last clustering, a synthetic report is generated. At the beginning of the report, a summaryindicates the number of factors found, and the minimum, average and maximum number of clusters,mean purity and contingency table fit.

This report describes, for each latent variable, the mean purity, the contingency table fit and the deviance.Those indices are described in the Correlation with Target Node's report. This new measure can beused to qualify the clustering result, to measure how well the Joint Probability Distribution is representedthrough each [Factor_i] variable.

It also describes the distribution of its values on the learning set, and the list of the nodes sorted accordingto the quantity of information brought to its knowledge (cf. Target analysis report). The final networkis automatically opened and the final database is associated with it. If the initial database contains a testset, it is also transferred and the missing value imputation is performed on the new [Factor_i] variables.At least, the final database is saved in the target directory.

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5.6. Policy learning of Static Bayesian networks

This menu item is only available in Validation mode for static networks having Decision nodes andUtility nodes. It makes possible to execute an algorithm based on dynamic programming to find theoptimal action policy. This policy describes the actions to apply in order to obtain the maximum expec-ted utility. The global utility is defined by the sum of all the utilities of the network. The resulting policycan be directly read in the quality table of each Decision node. The quality corresponds to the expectedutility if one applies the action and then applies the actions specified by BayesiaLab. The action to ap-ply, the one with the greatest quality, appears in light blue in the quality table and in the monitors.

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5.7. Policy Learning of Dynamic Bayesian networks

This functionality is only available in Validation mode for dynamic networks that have Decision nodesand Utility nodes. The temporal toolbar has then two new buttons:

The button activates Exploration (testing some random actions) during the temporal simulation. The button deactivates Exploration.

The button activates the Learning of the state/action qualities during the temporal simulation. The button deactivates Learning.

The parameters of the reinforcement learning algorithm that will update the quality of each state/actionpair based on the discounted sum of expected utilities can be changed by using the settings.

Caution

The complexity of this type of problems implies that it is impossible to guarantee that theobtained policy the optimal one. It is thus advised to carry out several tests and to keep thepolicy giving the best results.

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6. Inference

This menu gives access to:

• adaptive questionnaire over a network,

• interactive inference over a network,

• interactive Bayesian updating of a network,

• batch labeling of a network,

• batch inference over a network,

• batch most probable explanation labeling over a network,

• batch most probable explanation inference over a network,

• batch joint probability over a network,

• batch likelihood over a network,

• and allows choosing the inference type for the active network.

The different batch analysis can be performed on a database that will be loaded from a text file or a jdbcdatabase. Whatever the database is, it can't modify the structure of the network when it is imported,contrary to the classic database association. However, if a database is already associated with the net-work, these batch analyses can be performed on it.

Two inference methods are proposed:

• Exact inference by junction trees (by default)

• This inference method is based on the construction of a new structure (the junction tree) beforemaking the first inference.This construction can be time and memory costly depending on the networksize and connectivity. On the other side, once the junction tree is constructed, the inference isrealized very quickly. This tree has to be reconstructed after each modification of the network(structure or parameters).

• Approximate inference by Likelihood Weighting

• When the construction cost of the junction tree is prohibitive (not enough memory), it is possible touse approximate inference. This method is based on the law of large numbers and use networksimulation to approximate the probabilities.

While the exact inference cost appears in the junction tree construction (when passing from Modelingto Validation mode only), approximate inference requires very few memory but has a time cost at eachinference.

Some of the networks have a too important complexity to perform exact inference on them.The junctiontree may be too big to be represented in memory and the inference time can be extremely important. Inthis case, when the user asks to go in inference mode, a dialog box is displayed to propose severaloptions:

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• The use of the approximate inference avoids the memory size problem but the exactness of thecomputation is lost as well as some analyses that are design to work only with exact inference.

• A complexity reducing algorithm allows removing the less important arcs in the network. To do this,it uses the current database or generates one according to the probability distributions in order tocompute the importance of each arc in the network. The less important arcs will be removed until theexact inference becomes possible in memory and time.

• It is possible to go back to modeling mode in order to modify by hand the network structure to be usable.

• It is possible to continue with exact inference without take the warning into account.

6.1. Adaptive Questionnaire

The menu Adaptive Questionnaire launches the wizard depicted bellow for the specification of theoptions of the adaptive questionnaire.

It lets the user to indicate the target node and possibly a target state to perform an adaptive questionnairebased on a particular target value. It is also possible to precise the number of monitors to display (theordered list of questions), to force the removal of previous variable observations and to save these optionsin the BayesiaLab settings. This wizard also allows editing the costs associated with the observationof the variables.

Once the adaptive questionnaire is launched, a new toolbar is displayed:

The button resets the adaptive questionnaire.The button stops the adaptive questionnaire, deletesall the monitors and removes all the observations.

Adaptive questionnaire based on a target variable

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The adaptive questionnaire allows an automatic and dynamic organization of the monitors while takinginto account what information is being contributed to the knowledge of the target variable and the cor-responding cost of the questions. The target monitor appears with a pink background at the top of thelist, followed by the monitors ranked by their relevance.

The monitors of the observed variables appear at the end of the list (grayed) in the order of observation.The last observed variable then appears just after the last most relevant variable. It is possible to removean observation or to change the observed value by double-clicking on the monitor. It is also possible toobserve a variable that does not appear in the proposed list by monitoring it manually.

The translucent nodes are never proposed to the user.

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Adaptive questionnaire based on a particular state of the target variable

This questionnaire is similar to the previous one but the questions' worth is measured on the knowledgeof a particular value of the target variable, and not on the global knowledge of that variable. When thetarget is a variable only having two states, then these two questionnaires are equivalent.

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6.2. Interactive inference

The interactive inference allows using the associated database as an observation file. The associatedevidence scenario file can be also used. If the network has a database and an evidence scenario fileassociated at the same time, then a dialog box proposes to choose the data source to use. This modedisplays a new toolbar that allows navigating through the different cases contained in the database:

The button allows coming back to the first example of the data source; the button navigates to thelast one. The button goes to the previous example if it is possible and the button goes to the nextone. The text field indicates the index of the current example. It is possible to enter an index in the fieldto go to it directly. The button stops the interactive inference and removes all the observations. If theused data source is an evidence scenario file, the comment associated to each evidence set is displayedin the status bar of the network, if it exists. In the same way, if a database with row identifiers is used,they will be displayed in the status bar.

If the inference is done from an evidence scenario file, a right click on the index text field displays a listof the evidence sets contained in the file. A click on a line sets the corresponding observations:

If the inference is done from a database and this database contains row identifiers, a right click on theindex text field displays a new floating panel allowing the user to perform a search among the identifiers.The search is done thanks to a text field. The wildcards characters ? and * can be used. ? can replaceone and only one character. * can replace none or several characters.The Case Sensitive option allowsthe search to respect the case. After pressing enter, the search is performed and the list of the resultsis displayed. The number of corresponding rows is displayed at the bottom of the panel. A click on aline sets the corresponding observations:

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Caution

Sometimes a fixed probability distribution can't be done exactly because the algorithm usedto reach the target distribution fails to converge towards the target distribution. In this casea warning dialog box is displayed and an information message is also written in the console.

In the following picture, Cancer is the target node (pink background) and is not observed. The corres-ponding value in the database is No (blue sky) and corresponds to the value predicted by the network(99,97%).The node TbOrCa is not observed because it is declared as not observable (mauve background)and the corresponding value in the database is False (blue sky). The node Smoking is not observedbecause the corresponding value is missing in the database:

Thus, it is possible to see interactively the behavior of the network and to check its validity.

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6.3. Interactive Bayesian updating

The interactive Bayesian updating allows using the associated database as a file of observations. Theassociated evidence scenario file can be also used. If the network has a database and an evidencescenario file associated at the same time, then a dialog box proposes to choose the data source to use.This file can then be used to update the probability distribution of the nodes that have been declared as"not observable" (see costs), with respect to the observations that are interactively read from this file.Whereas the probability distribution of all the unobserved nodes can be impacted by these observations,we just update those of the "not observable" nodes after each observation. If the evidence scenario fileis used, it is possible to have an exact observation, a distribution of likelihoods or a distribution of prob-abilities (fixed distribution with exact inference or computation of the corresponding likelihoods with ap-proximate inference). This mode displays a new toolbar that allows performing a step-by-step updatingand also completing updating over the database:

The button allows coming back to the first example of the database and resetting the probability dis-tributions of the "not observable" nodes. The button performs an updating from the current index tothe last in the database. This process can be stopped while running by clicking on the red light of theStatus bar. The button steps to the next example. The text field indicates the index of the currentexample. It is possible to enter an index in the field to perform updating from the current index to thenew index. If the new index is lower than the current one, the probability distributions are reset and theupdating goes from the index 0 to the specified one. The button validates the updated conditionalprobability tables.The button stops the interactive updating and reinitializes the conditional probabilitytables. It also removes all the observations. Going back to the Modeling mode has the same effect. Ifthe used data source is an evidence scenario file, the comment associated to each evidence set is dis-played in the status bar of the network, if it exists. In the same way, if a database with row identifiers isused, they will be displayed in the status bar.

If the updating is done from an evidence scenario file, a right click on the index textfield displays a listof the evidence sets contained in the file. A click on a line performs the updating starting from the currentindex up to the specified index, taking into account the corresponding observations:

If the updating is done from a database and this database contains row identifiers, a right click on theindex text field displays a new floating panel allowing the user to perform a search among the identifiers.The search is done thanks to a text field. The wildcards characters ? and * can be used. ? can replaceone and only one character. * can replace none or several characters.The Case Sensitive option allowsthe search to respect the case. After pressing enter, the search is performed and the list of the resultsis displayed. The number of corresponding rows is displayed at the bottom of the panel. A click on aline performs the updating starting from the current index up to the specified index, taking into accountthe corresponding observations:

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Let us take an example with a network made of two nodes. The first node Alpha is continuous andcontains 10 intervals from 0 to 1. The other node named Measure is Boolean (its values are True andFalse) and is the son of Alpha.The conditional probability table of Measure is obtained from the probab-ilistic formula: P(?Measure?|?Alpha?) = If(?Measure?, ?Alpha?, 1-?Alpha?).

We associate with the network a database containing the values of the node Measure. After each obser-vation, the probability distribution of Alpha is updated to take into account its initial distribution and theset of all the observations of Measure that have been set. Here is a short simulation:

Initial distributions:

Example 0:

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Example 1:

Example 2:

...

Example 28:

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Caution

If "not observable" nodes are marginally independent but are linked to a common measurenode (directly or not), it is necessary to add an arc between these nodes to indicate theconditional dependence of these nodes knowing the observations. In the example below,we then have to simply add an arc between the hyper-parameters a and b of the Beta law,without modifying the conditional probability table to keep the marginal independence.

Caution


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6.4. Batch labeling

It makes an inference, for each case described in the specified database or in the associated evidencescenario file, to compute the most probable value of the target variable. When the target node has onlytwo states, a dialog box allows specifying the probability acceptance threshold (0.5 by default). In thecase of equal probabilities, the dialog box to choose a state allows specifying the choice policy:

The results are stored in an exploitation file that takes the selected fields of the input file and createstwo new fields: one for the predicted value, the other one for its corresponding probability.

If the data source is an external database, the fields of the input file that are included in the exploitationfile are selected via the wizard illustrated below:

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If the data source is the associated database, a dialog allows the user to choose on which part of thedatabase (all, learning or test) the operation is done and which nodes will be saved in the destinationfile. It is also possible to choose if the state's long names are used and if the continuous values aresaved:

The observations are done according to the cost of each node: if a node is not observable, it won't beobserved even if there is a corresponding value in the associated database.

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6.5. Batch inference

For each node declared as not observable (see costs), we compute, for each case described in thespecified database or in the associated evidence scenario file, the a posteriori probability distributionof the node.

The results are stored in an exploitation file that takes the selected fields of the input file and associates,for each state of each not observable node, the computed probability.The corresponding expected valueis also computed, if possible, for each not observable node and stored in the database. The expectedvalue is computed from the values associated with the states of the node. If there is no associated value,the expected values use the mean of each interval for a continuous node or the integer or real statesfor a discrete node. If it is not possible to compute these values, then, there is no expected value.



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6.6. Batch most probable explanation labeling

It makes an inference with the most probable explanation, for each case described in the specifieddatabase or in the associated evidence scenario file, and selects the most probable state of each targetvariable. The target variables are the nodes declared as not observable (see costs), target or hidden.

The results are stored in an exploitation file that takes the selected fields of the input file and createstwo new fields: one for the predicted value, the other one for its corresponding probability.



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6.7. Batch most probable explanation inference

For each node declared as not observable (see costs), target or hidden, we compute, for each casedescribed in the specified database or in the associated evidence scenario file, the most probableexplanation and all the likelihoods are saved.

The results are stored in an exploitation file that takes the selected fields of the input file and associates,for each state of each not observable node, the computed probability.



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6.8. Batch joint probability

For each record of the database or each evidence set of the associated evidence scenario file, thenodes are observed to the value of the record (except for the nodes declared as not observable andfor those where the value is missing). The joint probability of these evidences is computed with theBayesian network.

The results are stored in an exploitation file that takes the selected fields of the input file and associates,for each case, the computed joint probability of the evidences.



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Sorting the resulting file with respect to this joint probability can thus allow detecting the atypicalrecords, the outliers (cases with a very weak joint) by taking into account all the variables.

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6.9. Batch Likelihood

For each record of the database or in the associated evidence scenario file, the nodes are observedto the value of the record (except for the nodes declared as not observable and for those where thevalue is missing). The joint probability of these evidences is computed with the Bayesian network. Thenthe likelihood of this joint probability compared to the joint probability of the unconnected network iscomputed.

The results are stored in an exploitation file that takes the selected fields of the input file and associates,for each state of each not observable node, the computed probability.



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7. Analysis


• several graphic analysis tools that modify the graph view or display diagrams,

• several analysis reports,

• tools for displaying the edges, i.e. arcs that can be inverted,

• two tools for the performance evaluation of networks,

• a tool for the optimization of the target state.

• a target's optimization tree.

• a target's interpretation tree.

This menu is visible in validation mode only.

7.1. Graphical analysis

BayesiaLab offers a complete set of tools to graphically and interactively analyze a network.

Note that in various analysis, the translucent nodes are not taken into account.

Variable Clustering

This tool allows clustering the network variables into group of variables that are close semantically (fromthe Analysis menu or the shortcut ). These clusters are designed according to the node proximityin the graph and based on the force of the arcs. A color is automatically associated with each cluster tohighlight the clustering:

The number of clusters is automatically computed by using the force of the arcs. However, the associatedtoolbar contains a slider that allows choosing the desired number of clusters (4 in the previous example):

The button displays the hierarchical representation of the current clustering as a dendrogram. It is alwayspossible to modify interactively the number of clusters and to observe the result on the dendrogram. Acontextual menu allows displaying the comment associated with the node instead of the name.You canalso copy the graph as an image. The length of the links joining the clusters is inversely proportional to

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the strength of the relationships between the two sets of variables: more the link is short more the rela-tionship is strong.

When the cursor is moved over the junction point of the links, a tooltip containing the value of the linkbased on the arc force is displayed.

The button validates the current clustering and associates to each set of variables a class named[Factor_i]. When the button is pressed, a HTML report of the current clustering is displayed:

The button ends the variable clustering.

Once the classes created and associated with the clusters, it is possible to perform the multiple clus-tering, in modeling mode that allows, for each class named [Factor_i], generating a synthetic variablefrom the nodes belonging to this class.

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The number of clusters automatically determined by the algorithm can be limited by the convenient optionin the settings. The user can modify also the stop threshold corresponding to the max KL weight acluster can reach to be kep

Arc Force

It allows highlighting the importance of the arc with respect to the complete structure (from the Analysismenu or the shortcut ). The thickness of the arc is proportional to the importance of the probabilisticrelation; it represents in the total probability law.

You can use this tool to make translucent all the arcs having a force lower than the value indicated.

• Go back to the previous threshold

• Go to the next threshold

• Store the current arc forces in the arc comments if those comments are displayed.

• Stop analysis.

The KL force of each arc as well as its global contribution are displayed in the comment of the arcs.Youhave to press the button in the display tool bar in order to show them.

The filtered values are taken into account when the KL forces are computed.

Arc Mutual Information

The mutual information is computed for each arc of the network (from the Analysis menu or the short-cut ). It takes into account the filtered states.

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The thickness of an arc is directly proportional to the mutual information. Three values are displayed inthe arcs' comments:

• In black, the mutual information of the arc.

• In blue, the relative mutual information in the direction of the arc.

• In red, the relative mutual information in the opposite direction of the arc.

You can use the slider to change the arc display threshold:

• Go back to the previous threshold.

• Go to the next threshold.

• Store the mutual information in the comments of the arcs if those comments are displayed.

• Stop analysis.

If all the arcs of a node became transparent, the node becomes transparent.

Pearson's Correlation

The association of values to nodes' states allows computing R, the Pearson's linear correlation coeffi-cient between two nodes linked by an arc (from the Analysis menu or the shortcut ). If the statesdon't have associated values they can be generated from different ways:

• if the node is continuous the mean of each interval is used

• if the node is discrete with integer or real states, they are used as values

• otherwise, if there is no possibility to generate values, default values are defined in order to computeR (from 0 to n-1 for a node with n states).

Note: if there is no value associated with the states, the index of the state starting from 0 is used. If thenode is continuous, the used values are the mean of each interval. If the node is discrete with integervalues as states, the integer represented by the state is used.

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You can use the slider to change the arc display threshold according to the selected filter button:

• Go back to the previous threshold according to the selected correlation

• Go to the next threshold according to the selected correlation

• Displays only arcs having a negative correlation greater than the given threshold in absolute value

• Displays only arcs having a correlation greater than the given threshold in absolute value

• Displays only arcs having a positive correlation greater than the given threshold

• Store the current Pearson's correlations in the arc comments as well as the associated color ifthose comments are displayed.

• Stop analysis.

If all the arcs of a node became transparent, the node becomes transparent.

Node Force

It allows highlighting the importance of the node with respect to the complete structure (from the Ana-lysis menu or the shortcut ). Three kinds of node forces are computed:

• The entering node force: it is the sum of the force of the entering arcs.

• The outing node force: it is the sum of the force of the outing arcs.

• The global node force: it is the sum of the force of the entering arcs and the outing arcs.

You can use this tool to make translucent all the nodes having a force lower than the value indicated.

• Go back to the previous threshold according to the selected force

• Go to the next threshold according to the selected force

• Computes only the entering force of the nodes and displays if greater than the given threshold

• Computes the global force of the nodes and displays if greater than the given threshold

• Computes only the outing force of the nodes and displays if greater than the given threshold

• Stop analysis.

Correlations with the Target Node

It allows the visualization of the quantity of information brought by each node to the knowledge of thetarget node. The brightness of the squares appearing inside the nodes is proportional to this quantity ofinformation.

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Correlations with a State of the Target Node

It allows visualizing, for each node, two kinds of information relative to the target: the type of the probab-ilistic relation binding this variable and the target variable, and the information brought by each node tothe knowledge of the state of the target node

The symbol inside the node corresponds to the pattern of the probability distribution of the target value(CLUSTERS), conditionally to each value of this node.This symbol schematizes the probability distributioncurve (cf the pattern of node CATECHOL relative to the associated distribution, obtained by the meansof the contextual menu of node CATECHOL: Influence Analysis wrt target node

The symbol indicates that the distribution curve does not correspond to any of the four basic patterns.

Neighborhood Analysis

This kind of analysis allows visualizing, for the selected nodes, what is the set of nodes that are belongingto it according to the mode chosen in the toolbar:

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The nodes that are not belonging to the selected node are made translucent and are not selectableanymore. When we click on a visible node, the nodes that are not belonging to it are made translucent.In order to make the node visible again, you have just to click on any location except on a visible node.

It is possible to display, through the combo box:

• The Markov blanket

• The spouses

• The parents. It is possible to specify until which distance the ancestors are displayed with the corres-ponding field.

• The children. It is possible to specify until which distance the descendants are displayed with thecorresponding field.

• The neighbors. It is possible to specify until which distance the neighbors are displayed with the cor-responding field.

The number of displayed nodes is indicated in the status bar of the graph's window.

In the following example, the Markov blanket of the selected node is displayed, i.e. the not concernednodes are made translucent :

Mosaic Analysis

This analysis is used to display on a two-dimensional graph, the marginal probabilities of a node basedon all possible combinations of evidences set on nodes (from the Analysis menu or the short-cut + ). The Pearson's standardized residual is also computed for each combination. Theseprobabilities are displayed with colored rectangles that can be easily identified and compared to eachother.

The analysis is performed only on the selected nodes in the network.

Depending on the number of selected nodes, the dialog settings may slightly vary. The most completeversion is displayed when three nodes are selected. The following version is the simple version:

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The selected nodes are displayed in the table and their positions in the graph are displayed on the left.It is possible to modify their respective positions by selecting the desired node and using the Up andDown buttons.

By default the display of variables is done in alternating horizontal and vertical positions.With one variable,the graphic will represent P(Horizontal0). With two variables, the graphic will show P (Vertical0 | Hori-zontal0). With three variables, the graphic will display P(Horizontal1 | Vertical0, Horizontal0). With fourvariables, the graphic will display P(Vertical1 | Horizontal1, Vertical0, Horizontal0). And so forth.

If Horizontal Diagram is checked, then the graphic will be displayed with the first variable in verticalposition and all others in horizontal position inside a separate chart for each horizontal variable thatrepresents P (Vertical | Horizontal i). If Display P(Horizontal | Vertical) is checked, then each graphicwill represent P (Horizontal i | Vertical).

If a database is associated to the network, it is possible to choose the data source used to computethe standardized Pearson's residual:

• Network: the Structure Equivalent Example Number setting allows simulating a set of data in order tocompute the standardized Pearson's residual. This number is, by default, the number of examplesused to learn the network.

• Database: the standardized Pearson's residual is directly computed from the populations of the asso-ciated database.

If a database is associated to the network and one of the nodes is hidden (there is no data correspondingto the node) the default selected data source is the network.

If a database is associated to the network and it contains learning and test data, a combo box allowsus to choose which data will be used (all, learning or test).

The following image is a chart with three variables. The first variable is the horizontal variable Eyes, thesecond is the vertical variable Hair and the third is the horizontal variable Sex. The horizontal and ver-

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tical cells represent the marginal probabilities of each variable's states without any evidence set. Thecentral cells represent the conditional probabilities P(Eye | Hair, Sex).

For each cell, the standardized Pearson's residual is computed as : Di = (ni - Ni) / SQRT(Ni)

The Chi2 test equals the sum of Di2.

The value of the Chi2 test, the degree of freedom and the independence probability associated are dis-played at the top of the graph. It is possible to display the result of the G-test instead of Chi2 by modifyingthe corresponding settings in the preferences of the statistical tools.

A tooltip is displayed when the cursor hovers on each cell. It contains the list of the evidences corres-ponding to this cell as well as the joint probability and the conditional probability of the evidence. Thepopulation of the cell and the value of the residual are also displayed.

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The result display panel is also modifiable:

The option DisplayStandardizedPearson's Residual toggles between classic display with colors cor-responding to the states of the first horizontal variable and the display with the color code of the Pearson'sstandardized residual. The color code is as follows:

• simulated data are in very significant overrepresentation (D > 4)

• simulated data are in significant overrepresentation (D > 2)

• simulated data are in not significant overrepresentation (D > 0)

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• simulated data are in not significant under-representation (D < 0)

• simulated data are in significant under-representation (D < 2)

• simulated data are in very significant under-representation (D < 4)

• absence of simulated data

The option Resizable Graphic allows enlarging or reducing the graphic according to the window's size.If this option is unchecked, the graphic has a predefined constant size and scroll bars are displayed ifnecessary.

There are two possibilities of separation between the cells of the graph:

• Automatic Gap: it is computed according to the depth and the number of states of each variable.More the depth is important, more the gap is reduced.

• Constant Gap: we indicate what the number of pixels between two cells regardless of the depth ofthe variable is.

1. 1-dimensional charts:

On the left the simple chart and on the right the chart with the Pearson's standardized residual. Thewidth of cells corresponds to the marginal probability of each state of the horizontal variable. This isthe same as the monitor of this variable.


On the left the simple chart and on the right the chart with the Pearson's standardized residual. Thewidth of cells corresponds to the marginal probability of each state of the horizontal variable P(H).The height of the cells is the conditional probability of the vertical variable knowing the horizontalvariable P(V | H). The area of the cell represents the joint probability P(V, H).

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On the left the simple chart and on the right the chart with the Pearson's standardized residual. Thewidth of cells corresponds to P(H1 | V0, H0). The height of the cells represents the conditional prob-ability P(V0 | H0). The area of the cell represents the joint probability P(H1, V0, H0). The Pearson'sstandardized residuals show that, for example, the correlation between the fact of having blond hairand the fact of having blue eyes is very significant.When you have three selected variables, the dialogbox setup is modified to allow choosing how the Pearson's standardized residual will be computed.By default the Pearson's standardized residual is computed in relation to a fully unconnected network.It is possible to choose another reference model in the following combo box:

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Three models are available:

• The independence model:

• The conditional model 1:

• The conditional model 2:

So, we will compare with the addition of an arc between V0 and H1.

4. Horizontal charts:

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Above the simple chart and below the chart with the Pearson's standardized residual. This chartcorresponds to a sequence of 2-dimensional graphics involving the vertical variable and each hori-zontal variable. The width of cells corresponds to the marginal probability of the states of each hori-zontal variables P(Hi). The height of the cells is the conditional probability of the vertical variableknowing the horizontal variable P(V | Hi).

5. Inverted horizontal charts:

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Above the simple chart and below the chart with the Pearson's standardized residual. Like the previousone, this chart corresponds to a sequence of 2-dimensional graphics involving the vertical variableand each horizontal variable. However, instead of representing P(V | Hi), this chart represents P(Hi| V).The height of cells corresponds to the marginal probability of the states the vertical variable P(V).The width of the cells is the conditional probability of each horizontal variable knowing the verticalvariable P(Hi | V).

Influence Analysis wrt Target Node

This tool allows visualizing, for each target node's state, the influence of the other nodes in the network.This analysis is done only on the selected nodes or on all the nodes if no nodes are selected. If somenodes are not connected to the target, directly or not, they will be excluded from the analysis, as wellas the translucent nodes. This graph is dynamic, i.e. evidence can be set on the monitors and the graphwill be updated in order to reflect the modifications. The evidence context is displayed at the top of the

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graph, under the title. There are two kinds of display that can be chosen up to the checkbox InverseInfluence:

• Display of each target's state's probability knowing each state of each node:

The target's state's prior probability is shown by a red line.

• Display of each state's probability for each node knowing each one of the target's state:

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For each node, each state's prior probability is shown by a red line. In this mode, the nodes' currentvalues and delta are displayed in each "monitor". This value is computed from each node's valuesif they exist. If not, they are computed from the data for continuous nodes or from the intervals if nodata is associated. If the node has real or integer states, they will be used. Otherwise, integer valuesare automatically generated, starting from 0.

A checkbox Compute from Database is displayed if a database is associated to the network. It performsthe analysis not by using the bayesian inference anymore but by using the probabilities directly computedfrom the database.

A checkbox Fix References becomes available if Inverse Influenceis selected. It allows keeping thevalue of the a priori probability (red line) as reference if new evidence is set on the monitors. When thisoption is chosen, a priori is replaced by reference in the caption. This option is also available whendata are used. The computed delta values take into account the reference probabilities as well.

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When the mouse is moved over a bar chart, a tooltip displays the state's name and the associated ex-act probability.

It is possible to save the graph's image in a file or to print it.

When the colors associated with the nodes are displayed thanks to the convenient button, the bordersof each box are painted with the corresponding color.

The graph's contextual menu allows the user to:

• Sort the displayed nodes within three modes:

1. Default Order: the nodes' initial order is used or the displayed monitors' order, if they are monitored

2. Sort by Global mutual Information

3. Sort by Binary Mutual Information

• Display Comment Instead of Name

• Display States' Long Name

• Copy the image of the graph

Target Mean Analysis

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This tool allows you to graphically view the impact of changes in the selected nodes' means on the targetnode's mean. This lets you see the relationship between each node and the target variable in the formof curves. The translucent nodes are not taken into account.

For each node, its mean will vary from the minimum to the maximum of the variation domain and determ-ine, for each variation, the corresponding probability distribution up to MinXEnt method, in the samemanner as for the observation of a node's mean in the monitors. Each node will be observed withthis probability distribution and the corresponding value of the target node is calculated.

For each node the mean is computed from the values associated with the node: if the node has valuesassociated with its states, the mean is computed from them, otherwise if the node is continuous, itsmean is computed from the intervals, and if the node is discrete with integer or real states, the mean iscomputed from them. If there is no possibility to compute the mean, a default set of values from 0 to thenumber of states minus one is used.

A dialog box lets you configure the display of curves:

For the target variable, it is possible to display either the actual target's mean or the delta of the meanwith the prior target's mean.

Likewise for other variables, it is possible to display either the actual mean or the delta of the mean withthe prior mean. However, it is also possible to display the real variables' means, but all standardizedbetween 0 and 100.

The option Use Hard Evidences replace the previously used algorithm to compute the points of eachcurve simply by observing each node states and by determining the node's mean and the correspondingtarget's mean.

The option Order by Strength sorts the variables from the slope the more towards 90 degrees to theslope the more towards -90 degrees.This sort variables that have the most positive impact on the target'smean to the most negative impact. This slope is calculated at the midpoint of the curve. By default, thenodes are sorted according to the order of the corresponding monitors, if they exist.

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This figure represents the result of the previous settings. The legends are sorted according to the slopeof the curves.

When the mouse hovers on any of the points on the curves, a tooltip displays the name of the variablerepresented by the curve.The coordinates are displayed at the top of the window.The evidence context,if it exists, is also displayed at the top of the window.

The following figure represents the display of the deltas. A zoom has been done on the central points.The zoom is operated as in the scatter graph. It is also possible to change the curve's color by clickingon the colored square to the left of the node names in the legend.

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The chart's contextual menu allows the user to:

• Display Comment instead of Name

• Copy the image of the chart or the curves' points as text or html

• Print the image of the chart

Target Sensitivity Analysis

This tool allows visualizing graphically the impact of the network's variables over each state of the targetvariable. The variation range of each state is displayed according to each node's values. The rangesare sorted from bottom to top from the strongest to the weakest. The first thumbnail represents thevariations of the states on one graph. The following thumbnails represent the variations for each state.

The analysis is performed over the whole nodes or over a subset of selected nodes. The translucentnodes are not taken into account. The context of the observations is taken into account and displayedunder the graphs when it is necessary. The initial probability of each state is displayed at the bottom ofthe chart.

A contextual menu allows displaying the comment associated with the nodes instead of the name andalso the long names of the states. It allows copying the chart as an image.

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Parameters Sensitivity Analysis

This tool allows measuring the impact of the uncertainty associated with the "parameter" nodes on thetarget nodes by using sampling. By default, the parameters nodes are the root nodes (i.e. the nodeswithout parent), the target nodes are the leaf nodes (i.e. the nodes without child).

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The result of the simulation can be saved in a file. The result of the analysis is presented with a curverepresenting the repartition function of the probabilities of each state, and, a bar chart representing theprobability density function. Besides these graphical results, the mean and the standard-deviation of theprobabilities of the target states are also given. Obviously, the mean corresponds to the marginal prob-ability displayed in the monitors.

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The analysis is performed over the whole nodes or over a subset of selected nodes. The translucentnodes are not taken into account. The context of the evidences is taken into account and displayedunder the graphs.


Assessment Sensitivity Analysis

This tool allows, through sampling, visualizing graphically the impact of the different assessments ofnetwork's variables on each state of target variables. This tool is close to theparameter sensitivityanalysis.The following dialog box lets you choose the parameter nodes and target nodes and to indicatethe number of samples to be used:

The icon indicates that the node has assessments.

Three policies are available for sampling:

• Random selection of one expert per network: for each sample an expert will be drawn at randomand the conditional probability tables will be generated only with the assessments of the expert.

• Random selection of one expert per node: for each sample and for each node an expert will bedrawn at random and the conditional probability tables will be generated accordingly.

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• Random selection of an assessment per parent combination of each node: that is to say randomizean assessment by row of the conditional probability table. For each sample and each row of the tableof each node, an assessment is used to generate the probabilities of this line.

In each case, if there is no expertise that matches the sample, then the consensus is used.

For each target node, the result of the analysis is presented with a curve representing the repartitionfunction of the probabilities of each state, and, a bar chart representing the probability density function.Besides these graphical results, the mean and the standard-deviation of the probabilities of the targetstates are also given.

The user selects the node and the state to see by clicking on their tabs.

In this example, we have 32% chance that the state "Weak" of the node "TARGET" has a probabilitybetween 70% and 72.5%.

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The analysis is performed over the whole nodes or over a subset of selected nodes. The translucentnodes are not taken into account. The context of the evidences is taken into account and displayedunder the graphs.


Most Probable Explanation

This tool allows computing the most probable explanation, i.e. the case that has the highest joint prob-ability. The monitors are used to highlight this case. The probability of each state is then replaced bythe likelihood that the corresponding state belongs to most probable case.The context (i.e. the evidences)is taken into account during the analysis. Each time and evidence is set, the most probable explanationis computed and the monitors are updated.The joint probability displayed in the upper part of the windowof the monitors corresponds to the joint probability of this most probable explanation.

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The means and the standard deviations of the continuous nodes are no more computed and displayed.It is the same thing for the mean value, the total value and if necessary the uncertainty and the like-lihood which are no more computed and displayed in the information panel.

Edge Display (essential graphs and semi directed graphs)

Essential graphs are graphs in which there are directed arcs and edges (not directed arcs).The essentialgraph corresponding to a given Bayesian network is the graph in which the directed arcs correspond tothe arcs of the Bayesian network whose orientation cannot be changed without changing the probabil-istic relations encoded. Edges represent the arcs that can be inverted.

• Show Edges: This function, which is directly available via the key < E >, allows changing the arcswhose orientation can be modified while preserving the same probabilistic relations into edges. Theexample below illustrates a Bayesian network and the corresponding essential graph.

• Global Orientation of Edges: This function allows converting an essential, or semi directed graph,into a Bayesian network graph, by directing all the edges while preserving the same probabilistic rela-tions.This function is directly available via key < I >. It is also possible to direct specific edges by usingthe contextual menu associated with the arcs. The activation of this contextual menu on an edge or

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a previously directed edge allows its orientation/inversion. These arc orientations trigger thepropagation of the new information through the network so that the probability law remains identical,namely:

• orientation of the edges that cannot be inverted anymore,

• inversion of previously oriented arcs in order to preserve the probabilistic relations encoded by theinitial Bayesian network,

• removing of the orientation of the arcs that have been previously oriented threw propagation,

• changing of the conditional probability tables

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7.2. Analysis reports

BayesiaLab allows generating five different HTML analysis reports of a Bayesian network.

When a node has an associated comment, this node appears as a HTML link, and the comment canbe displayed by pointing on the node. This option can be modified in the Settings.

When a node has an associated color, this color is used as background of the cell where the name ofthe node is displayed. This option can be modified in the Settings.

When a node is continuous, the name of its states is followed by the index of the current state / the totalnumber of states, for example: Age:Young (1/3).

When a node is translucent, it is not taken into account in the various analysis.

Target Analysis Reports

Four different reports are available for target analysis:

• The correlation with target node

• The probability analysis wrt the target state

• The target dynamic profile

• The total effect on target

The target node must not have any evidence set or only soft evidences.

Correlation with Target Node

An analysis report is available for any target node (either by the mean of the Analysis menu, or directlyby using the shortcut . This HTML report has several sections:

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1. Context of the analysis

Description of the observed variables when the analysis is carried out.

2. Marginal probability distribution

Probability distribution of the target variable knowing the observed variables (context).

3. Distribution on the Learning Set

If a database is associated to the network, the target's probability distribution is computed on thedatabase.

4. Target Mean Purity

The target's mean purity is computed when a database is associated to the network. For each casein the database, we look if the network correctly determines the corresponding target's state presentin the database. The table below details state by state the results of the predictions. The columnNeighborhood indicates for what state the network was wrong and with the corresponding percentage.

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5. Performance Indices

Two performance indices of the network are computed if a database is associated:

a. Contingency Table Fit: Used to represent the degree of fit between the network's joint probabilitydistribution and the associated data. More the network correctly represents the database, the morethe value tends towards 100%. This measure, computed from the database's mean log-likelihoodis equal to 100% when the joint is completely represented in like in the fully connected network orto 0% when the joint is represented by a fully disconnected network. The dimensions representedby the not observable nodes are excluded from the computation.

b. Deviance: This measure is computed from the difference between the network's mean log-likelihoodand the database's mean log-likelihood. More the value tends towards 0 the more the network isclose to the database.

6. Node relative significance with respect to the information gain brought by the node to theknowledge of the target node

List of nodes, sorted by descending order according to the information they bring to the knowledgeof the target variable. The nodes that do not bring any information do not appear in this list. Thatcorresponds to the target node analysis.

a. Mutual Information: Amount of information brought by each variable to the target variable.

b. Mutual Information (%): Amount of information brought by each variable to the target variablecompared to an unconnected network.

c. Relative Significance: Ratio between the mutual information brought by each variable and thegreater mutual information.

d. Mean Value: Displays the nodes' mean value. Each node's mean is computed like this: if the nodehas values associated with its states, the mean is computed from them, otherwise if the node iscontinuous, its mean is computed from the intervals, and if the node is discrete with integer or realstates, the mean is computed from them. If there is no possibility to compute the mean, a defaultset of values from 0 to the number of states minus one is used.

e. Chi2-test or G-test: The independence tests Chi2 or G-test are computed from the networkbetween each variable and the target variable. It is possible to change the used independence testthanks to the statistical tool settings.

f. Degree of Freedom: Indicates the degree of freedom between each variable and the target variablein the network.

g. p-value: Represents the independence probability between each variable with the target variablein the network.

h. Chi or G-test on data: The independence tests Chi2 or G-test are computed as previously butfrom the associated database, if it exists.

i. Degree of Freedomon data: The degree of freedom is computed as previously but from the asso-ciated database, if it exists.

j. p-valueon data: The independence probability of the test is computed as previously but from theassociated database, if it exists.

7. Node relative significance with respect to the information gain brought by the node to theknowledge of the target value

For each value of the target, except for the filtered state, list of nodes, sorted by descending orderaccording to their relative contribution to the knowing of the target value (if the node has only two

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states, this list is identical to the preceding one). The nodes that do not bring any information do notappear in this list. That corresponds to the target state analysis.

a. BinaryMutual Information: Amount of information brought by each variable to the knowledge ofthe state of the target variable.

b. Binary Mutual Information (%): Amount of information brought by each variable to the knowledgeof the state of the target variable compared to an unconnected network.

c. Binary Relative Significance: Ratio between the mutual information brought by each variableand the greater mutual information.

d. Mean Value: Displays the nodes' mean value fro each target's state.

e. Modal Value: For each influencing node, description of the modal value (the most probable) withrespect to the context and the observed state of the target node. This modal value comes with itsprobability. This section allows establishing the profile of this target value.

f. A priori Modal Value: For each influencing node, description of the modal value when the targetnode is unobserved (but knowing the context). That makes it possible to define the profile whenthe target variable is unobserved.

g. Variation: Measure indicating the variation between the a priori modal value and the modal valuewhen we know what the value of the target variable is. The used formula is: -log2(P(X=modalvalue)) +log2(P(X=modal value|Target=observed value)). In Information Theory, this measurerepresents how many bits are won to represent the probability of X when the target value is known.Values printed in blue represent positive variations (the posterior probability of the modal value isgreater than the prior one) while values printed in red represent negative variations. Obviously, novariation is reported if the posterior modal value is different from the prior modal value. The modalvalue is then displayed in blue.

h. Maximal positive/negative variation: Measures indicating the states that have been the mostimpacted by the observation of the corresponding target state. The first one indicates the statewith the greatest increase whereas the second one indicates the state with the greatest decrease.

These measures correspond to the longest (right and left) grey arrows in the monitor (Inferencemode) showing the probability variation of states. These measures are particularly useful for thevariables that have more than two states!

When a node has an associated comment, this node appears as a HTML link, and the comment canbe displayed by pointing on the node.

If the target variable is a hidden variable, as it is the case for example for the variable Cluster inducedby data clustering, a button Mapping allows generating a mapping of the values of this variable.

A button Quadrants displays the Quadrant chart of the node's relative significance with the target relativelyto each node's mean:

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The points represent the variables. If a node has a color then the point will be displayed in this color.The node's name is displayed at the right of the point.When moving the mouse on the point, the coordin-ates are displayed in the top panel. The top panel shows the number of points displayed as well as theevidence context. It is possible to zoom in the chart as in the scatter of points.


• Display or not the nodes' comment instead of their names

• Copy the chart as image or as table of points (text or html)

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• Print the chart

The chart is automatically resized when the size of the window changes. This chart is cut into fourquadrants whose separations are:

• Along X-axis: the mean of the variables' means

• Along Y-axis: the mean of the relative significance of the nodes with the target

• Quadrant 1 : Top right: contains the important variables greater than the mean

• Quadrant 2 : Bottom right: contains the important variables few or not important but greater than themean

• Quadrant 3 : Bottom left: contains the few or not important variables that are below the mean

• Quadrant 4 : Top left: contains the important variables but that stay below the mean

It is possible to save the image of the chart in a file with the corresponding button.

Probability Analysis wrt the Target State

This analysis report is available for any target node (by the Analysis menu). It allows computing theimpact on the target state when slightly modifying one propability of a node's CPT. This is done for eachcell of each concerned conditional probability table.

The sensitivity function used is: P(h|e)(t)=P(h,e)(t)/P(e)(t) where h represents the hypothesis (TargetNode = Target State), e represents the context and t the probability.

The derivative of this function is computed as well as the minimal and maximal values when setting theprobability to 0% and 100%.

This HTML report has several sections:

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2. Probability of the target state

Probability of the target state knowing the observed variables (context).

3. Maximal Derivative

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This table summarizes the nodes with a maximal derivative different from zero. It is ordered from thegreatest to the smallest derivative.

4. Insensitive Nodes

This table contains the nodes with a derivative equal to zero.

5. Tables of sensitive nodes

For each sensitive node, a table represents each combination of its values and its parents' values.Each cell contains two parts:

• The part on the left indicates the derivative computed for each combination of states.The backgroundof the maximal derivative is yellow.

• The part on the right shows the probabilities of the target state when the probability of the a currentnode's state is set to 0% and to 100%. Obviously, those probabilities are symmetrical for binarynodes.

Target Dynamic Profile

This report allows establishing the profile of the target node according to the selected criterion (from theAnalysis menu or the shortcut + + ). The goal is to maximize or minimize one of the threeavailable criterions by setting evidence sequentially on the other variables. The parameters can bemodified in the following dialog box:

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Profile Search Criterion: One of these profile search criterions must be selected:

• Probability: For each state of the node, its associated probability will be maximized or minimized asneeded.

• Mean: The mean of the target node will be maximized or minimized as needed. If the node has valuesassociated with its states, the mean is computed from them, otherwise if the node is continuous, itsmean is computed from the intervals, and if the node is discrete with integer or real states, the meanis computed from them. If there is no possibility to compute the mean, a default set of values from 0

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to the number of states minus one is used. If the equivalent example number of the network exists,the 95% credible interval of the mean is computed and displayed in the report.

• Probability Difference between Two States: The algorithm tries to maximize or minimize the differ-ence between the probabilities between the selected states.

Criterion Optimization: In the criterion optimization area, the user can choose to minimize or maximizethe selected criterion. He can also take into account the probability of the evidence. In this case, thecomputed criterion is weighted by the probability associated with evidence that will be set. In the sameway, the costs associated with the nodes can be also taken into account.

Search Method: Four search methods for criterion optimization are available:

• Hard Evidences: Only hard evidences will be used for the optimization.

• Value/Mean Variations in %: The observation can be done either by fixing means, i.e. the convergencealgorithm will find, at each new observation, a probability distribution to obtain the wanted mean, orby fixing the probabilities, i.e. at startup, the probability distributions corresponding to the wantedmeans are computed once for all and will not change anymore. The observed means will vary in per-centage:

• Of the initial means of the nodes: Each driver variable will see its initial mean vary according to thegiven negative and positive percentages.The computed mean is bounded by the variable's variationdomain's limits.

• Of the variation domains of the nodes: Each driver variable will see its initial mean vary accordingto the given negative and positive percentages of the variable's variation domain. The computedmean is bounded by the variable's variation domain's limits.

• Of the margin progress of the nodes: Each driver variable will see its initial mean vary accordingto the percentages of the difference between the initial mean and the minimum of the domain andthe difference between the initial mean and the maximum of the domain.

Each node's mean is computed from the values associated to the states. If there is no associatedvalue, if the node is continuous, its mean will be computed from the intervals, and if the node is discretewith integer or real states, the mean is computed from them. If there is no possibility to compute themean, a default set of values from 0 to the number of states minus one is used. When an observedmean reach the limits of the variation domain of a node, the corresponding hard evidence is used in-stead. The percentages of the negative and positive variations of each node can be modified with themean variation editor.

In each case, the variables' filtered states will never be used.

Stop Criterion: The search is stopped when the joint probability of the network reaches zero. But thisstop criterion can be modified by setting a maximum number to the evidences done and by modifyingthe minimum joint probability allowed. It is also possible to use the automatic stop criterion that allowsfinding a good balance between search depth and usefulness of the levers.

Options: An option allows computing only prior variations, i.e. without cumulative effect: previous evidenceset will be removed before finding the best following evidence. It is also possible to associate to thenetwork the evidence scenario file corresponding to the found results. If an evidence scenario filealready exists, it can be replaced by the new one or the evidences can be appended to it.

Here is the result corresponding to the parameters above:

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In the report's window, in addition to the usual saving and printing options, a button Save Scenario allowsyou to save in a file the evidence scenario corresponding to the chosen optimization.

Total Effects on Target

This report allows computing the total effect of each variable on the target node (from the Analysismenu or the shortcut ). We consider that the target variable is locally linear and the total effect is theestimation of the derivative of the target with respect to this variable.The total effect represents the impactof a small modification of the "mean" of a variable over the "mean" of the target. The total effect is theobtained ratio. The standardized total effect is also displayed. It corresponds to the total effect multipliedby the ratio to the standard deviation of the current variable and the standard deviation of the target.

The mean of each node is computed like this: if the node has values associated with its states, the meanis computed from them, otherwise if the node is continuous, its mean is computed from the intervals,and if the node is discrete with integer or real states, the mean is computed from them. If there is nopossibility to compute the mean, a default set of values from 0 to the number of states minus one isused.

The positive impacts are displayed in blue and the negative ones are displayed in red.

After that, the independence test between the variables is computed:

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• Chi2-test or G-test: The independence tests Chi2 or G-test are computed from the networkbetween each variable and the target variable. It is possible to change the used independence testthanks to the statistical tool settings.

• Degree of Freedom: Indicates the degree of freedom between each variable and the target variablein the network.

• p-value: Represents the independence probability between each variable with the target variable inthe network.

If a database is associated to the network, so the computations of the independence test, the degreesof freedom and the p-value are also done on the data.

In addition to the saving and printing classical options, a button Quadrants allows displaying a Quadrantchart of the target's mean relatively to the total effect or the standardized total effect.The choice is donein the following dialog box:

The obtained result is purely illustrative, it can't really be analyzed:

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The points represent the variables. If a node has a color then the point will be displayed in this color.The name of the node is displayed at the right of the point. When moving the mouse on the point, thecoordinates are displayed in the top panel. The top panel shows the number of points displayed as wellas the evidence context.


• Display or not the nodes' comment instead of their names

• Copy the chart as image or as table of points (text or html)

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• Print the chart

The chart is automatically resized when the size of the window changes. This chart is cut into fourquadrants whose separations are:

• Along X-axis: the mean of the variables' means

• Along Y-axis: the mean of the criterion's importance (here the standardized total effect on the target)

Each quadrant has a specific meaning according to the knowledge represented by the bayesian network(marketing, satisfaction, etc.). In a general way, the quadrants are:

• Quadrant 1 : Top right: contains the important variables greater than the mean

• Quadrant 2 : Bottom right: contains the important variables few or not important but greater than themean

• Quadrant 3 : Bottom left: contains the few or not important variables that are below the mean

• Quadrant 4 : Top left: contains the important variables but that stay below the mean

It is possible to save the image of the chart in a file with the corresponding button.

Evidence Analysis Report

The Analysis menu or the shortcut + allow editing a report concerning the analysis of the setof observations. It can be hard evidence as well as probability distributions. It is possible to choose areference evidence by selecting an observed target node. This HTML report has several sections thatcan vary according to the presence of a reference evidence:

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2. Global contradiction measure

The measure that is used to determine if the observations are contradictory is defined by: log2( p(e1)p(e2) ... p(ej) / p(e1, e2, ..., ej)). When this measure is negative (blue background), i.e. when the jointprobability of the evidences is greater than the product of the marginal probability of these evidences,this means that the evidences globally support the same conclusion. Otherwise, when this measureis positive (red background), it means that we have globally contradictory evidences.This informationis only available for hard evidence.

3. Evidence analysis with respect to the reference evidence

The reference evidence is used to indicate the referential conclusion.

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a. Set of evidences that confirm the reference evidence

List of the evidences that confirm the reference evidence (blue).

b. Set of evidences that contradict the reference evidence

List of the evidences that contradict the reference evidence (red).

c. Set of neutral evidences

List of the evidences that do not confirm nor contradict the reference evidence (independent evid-ences).

Relationship Analysis Report

The Analysis menu or the shortcut + allow generating a report about the analysis of the set ofrelationships. The analysis process can be stopped at any moment and the report will be displayedcontaining only the already computed data.

If an arc is translucent, it is not taken into account in the analysis.

The first table represents the relationship analysis:

1. Kullback-Leibler divergence: This analysis computes the Kullback-Leibler divergence for each arcof the network. This distance is a measure of the differences between the probability distributionsrepresented by the network with the arc corresponding to the relation and without this arc. In thatcase, this measure is equal to the mutual information between the parent and the child. The relationsare displayed with respect to their importance, in the decreasing order.The computed Kullback-Leiblerdivergence takes into account the possible filtered states of the parent and the child.

2. Relative Weight: The relative weight of each relationship.

3. Global Contribution: The Kullback-Leibler divergence global contribution percentage of each arc isalso displayed.

4. Mutual Information: Represents the quantity of information brought by each variable to the other.

5. GKL-test:The independence test G is computed from the Kullback-Leibler divergence of the relation-ship. Its value is thus computed from the network. The filtered values are taken into account whenthe KL divergences are computed.

6. Degree of Freedom: Represents the degree of freedom of the relationship. It is used to compute theindependence probability.

7. p-value: Represents the independence probability of the GKL-test computed on the network for eachrelationship.

8. Khi2-test or G-test on the data: If there are data associated to the network, the independence testsChi2 or G-test are computed from these data for each relationship. It is possible to change the usedindependence test thanks to the statistical tool settings.The weights of the database are taken intoaccount.

9. Degree of Freedom on the data: Represents the degree of freedom of the relationship computedfrom the associated data.

10. p-value on the data: It is computed from the independence test on the data and from the degree offreedom on the data. It represents the independence probability of the Chi -test or G-test for eachrelationship.

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11. Pearson's Correlation: The Pearson's Correlation is displayed for each arc.

The second table represents the node force analysis. For each node it displays:

1. Outing Force: It corresponds to the sum of the forces of the outing arcs of each node.

2. Entering Force: It corresponds to the sum of the forces of the entering arcs of each node.

3. Global Force: It corresponds to the sum of the forces of both the entering and outing arcs of eachnode.

Hidden Variable Discovery

This report allows computing the G-test and the independence probability between two variables of thenetwork bounded by a path of length one or two and which is not a V-structure (Analysis menu). All theexisting paths of length one or two (without V-structure) will be tested. The independence probabilitywill be computed and only the paths which are not independent are kept in the report.

Computing independence between variables:

• G-test: The value of the independence test G is computed from the data associated with the networkbetween each pair of variables which are the ends of the paths.

• Degree of freedom: Indicates the degree of freedom between the ends of each path.

• p-value : Represents the independence probability of the G-test between the ends of each path.

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7.3. Network Performance

7.3.1. Network Targeted Performance

This tool uses associated database to evaluate the quality of the active Bayesian network for the predictionof the target variable.

If the database contains data for learning and for test, the analysis is done only over the test data;otherwise it is done over the whole data.

If the database contains weights, they are taken into account for the evaluation.

This evaluation can be performed either on only one state of the target either on all states.

When the target node has only two states, a dialog box allows specifying the probability acceptancethreshold. It is possible to define a unique threshold (0.5 by default) that we can modify or to use severalthresholds for the evaluation. We indicate the wanted threshold number and the algorithm choose theprobability thresholds by following an equal frequency distribution. The following dialog box allows en-tering the parameters for the evaluation:

In the case of equal probabilities, the following dialog box allows specifying the choice policy:

The obtained result for multiple acceptance thresholds:

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When the evaluation on multiple thresholds is selected, it is possible to display the confusion matricesaccording to each threshold by selecting the threshold wanted in the box of choice called Acceptancethreshold.

The obtained result for multiple states:

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There is one thumbnail for each evaluated state. It allows displaying the curves corresponding to eachstate.

As the above figure shows it, the evaluation is carried out by four complementary tools. A total precisionof the model (function of the number of correct predictions of the target variable), a Confusion Matrixin which figure the occurrence number, the reliability and precision of each prediction, and finally thegain curve, the lift curve and the ROC curve centered on the target value.

At the top of the report, the Total Precision of the network is specified. Below that, two indices aredisplayed, in order to measure the quality of the numerical prediction:

• R: the Pearson coefficient

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• R2: the square value of the Pearson coefficient

The button Global report allows generating a HTML report that contains, for each acceptance threshold,the total precision and the corresponding confusion matrices. It indicates, for each state, the computedGini index, Relative Gini index, Mean Lift and the Relative Lift index. It contains also the Relative GiniGlobal Mean and the Relative Lift Global Mean. Below, the total precision, the Pearson's coefficient andits square value are added.

Confusion Matrix

The direct evaluation of a network modeled for the prediction of a target variable can be realized bycomputing its total precision, i.e. the ratio between the number of correct predictions and the total numberof cases. This measure is useful but can be too general. The Confusion Matrix proposed by BayesiaLaballows having a more precise feedback about the model performances. The predictions of the modelappear on the lines, the column representing the real values that are in the database (the model has

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predicted 723 C in the following matrix, whereas there are 730 C in the file). Three visualization modesare available:

1. Occurrence Matrix: number of cases for each Prediction/Real value

2. Reliability Matrix: ratio between each prediction and the total number of the corresponding prediction(the sum of the line)

3. Precision Matrix: ratio between each prediction and the total number of the corresponding real value(the sum of the column)

A right click on the matrix allows copying it into the clipboard. It is then possible to paste it directly asan image, or to paste it as a data array.

Gain Curve

When one is faced to the problem of predicting the value of a particular variable (the value of the targetnode), the evaluation of the model can be realized by using the gain curve.

The Gain curve is generated by sorting, in the decreasing order, the individuals according to the targetvalue probability returned by the network, e.g. the appetence/fraud/churn probability.The X-axis representsthe rate of individuals that are taken into account. The Y-axis represents the rate of individuals with thetarget value that have been identified as such.

In the Gain curve below, there are almost 5% of individuals that have the target value (yellow). The bluecurve represents the gain curve of a pure random policy, i.e. choosing the individuals without any order.The red curve represents the gain curve corresponding to the optimal policy, i.e. where the individualsare sorted according to the perfect model. Choosing the first 5% of individuals allows then getting 100%of the individuals with the target variable with the optimal policy, against only 5% with the random policy.

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A left click on the graphical zone of the curve allows getting the exact coordinates of the correspondingpoint and the probability of the target value of the associated case.

For example, the screen shot below indicates that the selection of the first 5.87% cases imply a detectionrate of 79.71%. It also indicates that the last case of that selection has a probability of having the targetvalue equals to 52.13%.

The Gini Index and the Relative Gini Index are computed according to the curve and displayed at thetop of the graphic. The Gini Index is computed as the surface under the red curve and above the bluecurve divided by the surface above the blue curve. But, as shown above, the surface of the optimalpolicy is less than the surface above the blue line, so the relative Gini index is computed as the surfaceunder the red curve and above the blue curve divided by the surface under the curve of the optimalpolicy and above the blue curve. It is a more representative coefficient.

This interactive curve is not only an evaluation tool. It is also a decision support tool that allows definingthe best probability threshold from which an individual will be considered as belonging to the target.

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A right click on the graphical zone allows choosing between printing the curve and copying it to theclipboard. In the last case, it is then possible to paste it directly as an image, or to paste the correspondingdata points.

The gain curve has a tool used to automatically analyze the expected economical gains with the evaluatedmodel.These computations follow the definition of the unit costs corresponding to the treatment of eachindividual (x-axis), of unit gains corresponding to each positive answer (y-axis), and finally of a targetpopulation's size.The economical gain is then defined as the difference between the profit correspondingto the treatment of x% of the population and the profit corresponding to the treatment of the whole pop-ulation. As the following screen captures shows it, the result is displayed as a curve (blue curve) andas a gradient of color (the closer we are to the yellow, the more we are close to optimality).

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The economical parameters can be modified with the following dialog:

Lift curve

When one is faced to the problem of predicting the value of a particular variable (the value of the targetnode), the evaluation of the model is often realized by using the lift curve.

This curve comes from the Gain curve and highlights the improvement between the policy returned bythe current Bayesian network and the random policy. The X-axis represents the rate of individuals thatare taken into account. The Y-axis represents the lift factor defined as the ratio between the rate of thetargeted population obtained with the current policy and the rate obtained with the random policy.

The curve below is the optimal Lift curve corresponding to the first Gain curve.The best lift value, 20.88,is defined as the ratio between 100% and 4.8% (optimal policy/random policy). The lift decreases thenwhen more than 4.8% of the individuals are considered, and is equal to 1 when all the individuals aretaken into account.

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On a real example the Lift curve looks like this:

The Mean Lift and the Relative Lift Index are computed according to the curve and displayed at the topof the graphic.The Mean Lift is the mean of all the points in the curve.The relative Lift Index is computedas the surface under the Lift curve divided by the surface under the lift curve of the optimal policy.

ROC Curve (Receiver Operating Characteristic)

When one is faced to the problem of predicting the value of a particular variable, the evaluation of theBayesian network can be realized by using a ROC Curve.

This graph is a plot of the True Positive Rate (Y-axis) against the False Positive Rate (X-axis). A pointof the curve corresponds to the result obtained by using a particular threshold (a probability value) forthe decision rule (i.e. to decide if the case has the target value or not based on the threshold and itsprobability to have the target value: p(case) >= threshold).

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The following figure depicts the ROC curve corresponding to an optimal model. In fact, the optimal curveindicates that all the cases with the target value have a probability greater than those without this targetvalue.

A left click on the graphical zone of the curve allows obtaining the exact coordinates of the correspondingpoint and the value of the corresponding threshold.

For example, the screen shot below indicates that a threshold of 53.13% implies a detection rate of79.89% with 1.59% of false positive examples.

The ROC index is computed according to the curve and displayed at the top of the graphic. It representsthe surface under the ROC curve divided by the total surface.

A right click on the graphical zone allows choosing between printing the curve and copying the curve tothe clipboard. In the last case, it is possible to paste directly the curve as an image, or to paste the datapoints corresponding to the curve.

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7.3.2. Network global performance (Log-likelihood)

This tool computes a global performance index of the network over the associated database. The com-puted value corresponds to the log-likelihood.

If the database contains data for learning and for test, the analysis is done for each kind of database;otherwise it is done over the whole data. When a test database is associated with the network, we cancompare the result obtained over the learning database with the result over the test database in a thirdthumbnail where the results are superimposed in order to analyze the differences.

The results are displayed as graphs in a window. There is a thumbnail for each kind of database(learning and test) and one more for the comparison. For each database, it is possible to visualize theresults as a density function in which the interval number can be modified dynamically or as a distributionfunction.

For each panel, the mean, standard deviation, minimum, maximum and computed row numbers are in-dicated below the chart. In addition, two performance indices are displayed:

• Contingency Table Fit: Used to represent the degree of fit between the network's joint probabilitydistribution and the associated data. More the network correctly represents the database, the morethe value tends towards 100%. This measure, computed from the database's mean log-likelihood isequal to 100% when the joint is completely represented in like in the fully connected network or to 0%when the joint is represented by a fully disconnected network. The dimensions represented by thenot observable nodes are excluded from the computation.

• Deviance: This measure is computed from the difference between the network's mean log-likelihoodand the database's mean log-likelihood. More the value tends towards 0 the more the network is closeto the database.

• Kolmogorov-Smirnov Test: The test used is the test of distribution adequacy between the twosamples. This test is only computed in the comparison panels. It compares the two distributions oflog-likelihoods. The values Z, D and the corresponding p-value are displayed.

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Density function for the test database

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Comparison between density functions for the learning and the test databases

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The results for learning are always represented in red and the results for test in green.The transparencyof the display for test results allows showing the learning results under. Both functions are at the samescale.

Distribution function for the learning database

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Distribution function for the test database

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Comparison between the learning and test distribution functions

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The results for learning are always represented in red and the results for test in green. The learning andtest database graphics have the same vertical scale but don't have a common horizontal scale. Thesecurves are represented horizontally with the computed line percent of their own database.

When an example of a database is impossible, i.e. it represents an impossible combination of evidences;the example is not taken in account in the final result and is displayed in a table in a HTML report. Thisreport is displayed by pressing on the Skipped Rows button.

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The button Extract Database allows saving only the examples of the database with log-likelihood con-tained in the interval specified in the following dialog box. The other parameters are the same as fordatabase saving:

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7.4. Target Optimization

This function allows searching for the tuples that either optimize the probability of the target state (likeli-hood maximization) or optimize the mean value of the target node.

You can choose to maximize or minimize the criterion. A checkbox allows taking the joint probability ofthe evidence during the search. In this case, we will optimize the a posteriori (probability of the targetstate knowing the tuple weighted by the occurrence probability of that tuple). In the same way, the costof evidence can be taken into account. The context (i.e. the evidence) is taken into account during theanalysis.

Several search methods are available:

• By hard evidence on nodes' states.

• By observation of the value/mean of the nodes.The observation can be done either by fixing means,i.e. the convergence algorithm will find, at each new observation, a probability distribution to obtainthe wanted mean, or by fixing the probabilities, i.e. at startup, the probability distributions correspondingto the wanted means are computed once for all and will not change anymore. The observed meanswill vary in percentage:

• Of the initial means of the nodes

• Of the variation domains of the nodes

• Of the margin progress of the nodes, i.e. the difference between the initial mean and the minimumof the domain and the difference between the initial mean and the maximum of the domain.

The percentages of the negative and positive variations of each node can be modified with the meanvariation editor.

The settings panel allows restricting the search to the selected nodes. The size of the evidence is thesize of the tuples we want to obtain.

This is an any-time algorithm. In other words, even if this is an exhaustive search over the tuples, it canbe interrupted at any moment by clicking on the red light (at the lower left corner of the graph window)without losing the results. Furthermore, we use a heuristic that allows us to begin the search with themost promising tuples.

You can save the found tuples in an evidence scenario file: just choose the number of examples wewant to associate or choose to associate all the obtained combinations. If the search is stopped beforethe end, we won't obtain the wanted number of examples.

If an evidence file is already associated, you can choose to replace it or to append the examples at theend.

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The filtered states are not taken into account during the search.

A dialog box indicates the end of the optimization.

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7.5. Target Optimization Tree

This function allows searching for several policies in order to optimize the target node. Two options areavailable:

• Optimization of the specified target state

• Optimization of the target's mean

Its functionning is similar to the target dynamic profile except that instead of finding only the "optimalpolicy" it tests also alternative optimization policies. The algorithm finds the best evidence on a node tooptimize the target (state or mean). Once this node found, two branches in the tree are created:

• the left branch has the node observed and it stays observed in the subtree

• the right branch has no observation, and this node cannot be observed anymore in this subtree. It iscalled an alternate tree.

For each branch, the search is done again on the remaining nodes with the same rules until one of thestop criterions is obtained or no more node is available.

The filtered states are not taken into account in the search.

The following panel allows entering all the parameters:

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Target:

You can select the target node. By default, the current target node is used. After that, you can chooseto optimize the selected target state or the mean.

Criterion Optimization:

You can choose to maximize or minimize the criterion. A checkbox allows taking the joint probability ofthe evidence into account during the search. In this case, we will optimize the a posteriori (probabilityof the target state knowing the evidence weighted by the occurrence probability of that evidence). In the

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same way, the cost of evidence can be taken into account. The observation context is also taken intoaccount during the analysis.

Search Method:








Search Stop Criterions:

The settings panel allows restricting the search with four different stop criterions that can be combined.

• You can specify the maximum number of nodes that can be observed in a branch of the tree.

• You can also specify the maximum number of alternate trees allowed. Alternate trees correspond tothe nodes that are skipped in the right branches of the tree.

• The algorithm can stop also when an evidence reaches the minimum joint probability allowed.

• The automatic stop criterion is an heuristic test that allows us to find a good balance between theoptimization due to an evidence and the impact on the joint probability.

Output:

The results will be associated as evidence scenario file. Each branch of the tree corresponds to a lineof evidence in the evidence scenario file.


Results:

The results are displayed in a binary tree. Each node of the tree represents the node chosen by the al-gorithm.

The evidence context will be displayed at the top if necessary.

A node contains four parts:

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• The name or comment of the target node. The used background is the node's color.

• The probability of the target state of the target node before setting the evidence if we optimize thetarget state or the mean of the target node before setting the evidence if we optimize the mean.

• The joint probability before setting the evidence.

• If the node is not a leaf, the name or comment of the chosen node that will be observed. The usedbackground is the node's color. Otherwise, it shows the value of the optimization score with a whitebackground. The last node of the "optimal branch" has a thick red border in order to find it quickly.

Two kinds of branches exist:

• The left branches on which the chosen nodes are observed. If hard evidence is used, the name ofthe observed state is displayed on the branch. If the mean is observed, the value of the mean of thechosen node is displayed. If this mean corresponds to the negative variation, it is displayed in red,otherwise, if it is the positive variation, it is displayed in blue.

• The right branches represent that the chosen node is not observed and skipped. It won't be used inthe corresponding subtree.

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Toolbar:

The toolbar at the top of the window allows the user:

• To zoom in the tree

• To zoom out the tree

• To go back to the initial zoom

• To fit the tree to the window

• To display the tree horizontally

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Actions:

The buttons at the bottom of the windows allow closing the window, saving the image, printing the treeand displaying the report.

The contextual menu allows:

• Displaying the comment instead of the name of the nodes

• Displaying the long names of the states

• Copying the tree as an image or as html. The html copy reproduces the vertical display as well as thehorizontal one. The displayed colors are also used.

It is possible to perform a manual zoom by clicking and dragging the mouse to select the area that willbe zoomed in.The shortcut + mousewheel performs zooming (and unzooming) on the tree centeredon the cursor.

Moving the mouse over a node displays a tooltip containing the chain of evidence done until this node.

A double-click on a node closes its subtrees in the window. Double-click on it to display them again.

Report:

Depending on the options, the button Report displays an html report containing the list of the best chosennodes in the whole tree with their best observation and the corresponding optimization score.

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7.6. Target Interpretation Tree

This function allows generating a tree that helps interpreting the target node. The algorithm optimizesthe knowledge of the target by reducing its corresponding entropy (or binary entropy if we choose aspecific state with the "Center on State" option). We are then using the (binary) mutual information tobuild the tree (that can be combined with the cost associated to the nodes).

The Adaptive Questionnaire is functionally close to that tree. If the user always choose the first variable,the sequence of the questionnaire is described in that tree. Once the algorithm has found a node, nbranches, corresponding to the n states of the node, are created in the tree if hard evidence is used,otherwise, two branches, correponding to the negative and positive variations of the mean, are createdif the mean variations are used. On each branch the observed state or mean is displayed.

For each branch, the search is done again on the remaining nodes with the same rules until one of thestop criterions is obtained or no more node is available.

The filtered states are not taken into account in the search.

The following panel allows entering all the parameters:

Target :

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You can select the target node. By default, the current target node is used. After that, you can chooseto center the search on a specific state or not.

Search Method:








A checkbox allows taking the cost of the evidence into account during the search by dividing the scorebased on the mutual information.

The observation context is also taken into account during the analysis.

Search Stop Criterions:

The settings panel allows restricting the search with three different stop criterions that can be combined.

• You can specify the maximum number of nodes that can be observed in a branch of the tree.

• The algorithm can stop also when an evidence reaches the minimum joint probability allowed.

• The automatic stop criterion is the value of the conditional mutual information (divided by the cost ifthe cost option is checked). The algorithm stops if this value is lower than the given parameter.

Output:

The results will be associated as evidence scenario file. Each branch of the tree corresponds to a lineof evidence in the evidence scenario file.


Results:

The results are displayed in a binary tree if the mean variations are used or in a n-ary tree if hard evidenceis used. Each node of the tree represents the node chosen by the algorithm.

The evidence context will be displayed at the top if necessary.

Nodes are very similar to monitors. A node contains four parts:

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• The name or comment of the target node. The used background is the node's color.

• The value of the node with its delta and the joint probability with its delta before setting the evidence.

• The probability distribution of the target node before setting the evidence. Each state with the corres-ponding probability is displayed as in the monitor. If the search is centered on a state, this state ispainted in light blue.

• If the node is not a leaf, the name or comment of the chosen node that will be observed. The usedbackground is the node's color. The score based on the mutual information (divided by the cost if thecost option is checked) is displayed in percentage.

If hard evidence is used, the name of the observed state is displayed on the branch. If the mean is ob-served, the value of the mean of the chosen node is displayed. If this mean corresponds to the negativevariation, it is displayed in red, otherwise, if it is the positive variation, it is displayed in blue.

Toolbar:

The toolbar at the top of the window allows the user:

• To zoom in the tree

• To zoom out the tree

• To go back to the initial zoom

• To fit the tree to the window

• To display the tree horizontally

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Actions:

The buttons at the bottom of the windows allow closing the window, saving the image and printing thetree.

The contextual menu allows:

• Displaying the comment instead of the name of the nodes

• Displaying the long names of the states

• Copying the tree as an image or as html. The html copy reproduces the vertical display as well as thehorizontal one. The displayed colors are also used.

It is possible to perform a manual zoom by clicking and dragging the mouse to select the area that willbe zoomed in.The shortcut + mousewheel performs zooming (and unzooming) on the tree centeredon the cursor.

Moving the mouse over a node displays a tooltip containing the chain of evidence done until this node.

A double-click on a node closes its subtrees in the window. Double-click on it to display them again.

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8. Monitor


• Monitors Sorted wrt Target Variable Correlations: displays the monitors sorted wrt the targetvariable correlations. If a subset of nodes is selected in the graph, this function is restricted to themonitors of those nodes. If some nodes are translucent, their monitors are not displayed.

• Monitors Sorted wrt Target Value Correlations: displays the monitors sorted wrt the target valuecorrelations. If a subset of nodes is selected in the graph, this function is restricted to the monitors ofthose nodes. If some nodes are translucent, their monitors are not displayed.

• Sort by Less Probable Evidence: displays the monitors corresponding to the observed nodes orderedfrom the less probable evidence (that degrades the most the joint probability) to the most probableevidence. Considering that the current network represents mainly the "normal cases", this tool is thenvery useful to diagnose the variables that have caused a very low joint probability (atypical cases wrtthe given network).

• Sort Monitors by Name: displays the monitors under increasing lexicographic order of their namesor comments (if comments are displayed instead of names).

• Zoom: zooming the monitors

• Zoom In: increase the size of the monitors.

• Zoom Out: decrease the size of the monitors.

• Default Zoom: go back to the default zoom level.

• Remove All Observations: removes all the observations.

• Delete All: deletes all the monitors.

• Reset the Probabilities Variations: remove all probability shifts.

• Fix the Reference Probabilities: referencing of the probability shifts

• Hilghlight the Probability Maximum Variations: displays the maximum probability shifts.

• Store Evidence Scenario: adds the current set of evidences to the current evidence scenariofile.

• Select All: selects all the monitors.

• Display Comment Instead of Name: displays the comment associated with the node instead of thename in the monitor. If the comment is too long, it will be truncated like the name would be.This optionis saved with the network.

• Display the States' Long Name: displays the long name eventually associated with the nodes' statesinstead of the states' name. When a state does not have a long name associated, its own name isused instead. If the long name is too long, it will be truncated as the states' name would be.This optionis saved with the network.

• Display Probabilities with Scientific Notation: displays the probabilities in scientific notation in themonitors and in the monitors' tooltips. This option is saved with the network.

• Fit Monitor Widths to Content: enlarge the monitors in order to display the whole content withoutcropping the names. This action is done only on the displayed monitors. If a new monitor is displayedand its width is greater, you must click on it again.

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• Restore Default Monitor Widths: restore the witdh of the monitors to the default value.

• Display the Uncertainty and Likelihood Variations: displays in the information panel the uncertaintyand likelihood variations due to the evidences that were set.

This menu is visible in validation mode only.

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9. Tools

• Compare (any mode):

• Structure: starts the structure comparison tool of two networks.

• Joint: starts the joint probabilities comparison tool.

• Cross Validation (validation mode):

• Arc Confidence: starts the arc confidence analysis tool on the current network. This networkmust have an associated database.

• Data Perturbation: starts the data perturbation tool on the current network. This network musthave a database associated with it.

• Targeted: starts the targeted cross validation tool on the current network. This network musthave a database associated with it and a target node.

• Structural Coefficient Analysis: starts the structural coefficient analysis tool on the currentnetwork. This network must have a database associated with it.

• Multi Quadrant Analysis (validation mode): starts the multi-quadrant analysis tool on the currentnetwork. This network must have an associated database.

• Assessment (any mode): it is available only if experts are registered on this network and assessmentshave been done

• Export a Network per Expert: the user select a destination directory. For each expert, a networkwith the same structure but with the probabilities given only by this expert will be saved in this dir-ectory.When there is no probability given by this expert, the consensus of the other experts is used.

• Export Probability Assessments: exports into a database all the assessments done by the experts.The database contains a column for each node with assessments, a column with the correpondingprobability given by the expert, a column for the confidence of this assessment and also the nameof the expert and the time used to do this assessment (see Assessments).

• Export Expert Assessments: exports into a database for each cell of each table with assessments,the probability given by each expert and the associated confidence. Then, there are two columnsby expert, one for the probability and the other for the confidence. A column Weight give a weightto each row corresponding to 1 / number of states (see Assessments).

9.1. Network Comparison

Two Bayesian networks can be compared by using the Tools>Comparison menu item. The nodes formboth networks must be exactly the same.

Parameters

This dialog box allows choosing the networks to be compared:

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The left hand side network is the "reference" network for comparison. Clicking the button below thepicture allows loading another reference network.

The right hand side network is the "comparison" network. On the same manner, clicking the button belowthe picture allows loading another network.

An option allows choosing whether the Bayesian networks themselves or their equivalence class shallbe compared.

Comparison report

The following report (HTML format) is created by clicking Compare button:

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The first line indicates the names of compared networks.

The rest of the report contains up to ten lists:

• Common arcs: same arcs in networks

• Inverted arcs: arcs which orientation changes in the comparison network

• Added arcs: arcs that exist only in the comparison network

• Deleted arcs: arcs that exist only in the reference network

• Common edges: same edges in networks

• Added edges: edges that exist only in the comparison network

• Deleted edges: edges that exist only in the reference network

• Common V-Structures: same V-Structures in networks

• Added V-Structures: V-Structures that exist only in the comparison network

• Deleted V-Structures: V-Structures that exists only in the reference network

Graphs

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The Graphs button from the report allows displaying the structure comparison graphic tool. With thistool, the data from the report can be easily viewed.

9.1.1. Graphical Structure Comparator

This tool can be acceded from the results of three different kinds of analysis:

• Simple network comparison

• Arcs confidence analysis

• Targeted cross validation

The purpose of this tool is comparing a "reference" network with another one or a group of other ones(or their equivalence class). It creates a colored graphical structure (that is not a Bayesian network)representing all differences between networks.

The patterns matched are arcs, edges and V-Structures.

Toolbar

The window toolbar contains eleven buttons: 4 for the navigation, 6 for modifying display and one tosave networks

1. Navigation bar

• displays synthesis structure

• displays reference structure

• displays the previous structure (with regards to current displayed)

• displays the next structure (with regards to current displayed)Navigating through the structures is realized in this order:

a. Synthesis structure

b. Reference structure

c. 1st comparison structure

d. 2nd comparison structure

e. ...

2. Display bar

• Zoom in

• Zoom out

• Display structure with default zoom

• Adjust zoom to window size

• Rotating structure on the left

• Rotating structure on the right

3. Save bar

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Save the current displayed network. This option is only available for comparison structures. Itis disabled for Synthesis and Reference structures.

•

This button positions the graph in the window.

Popup menu

Popup menu allows displaying nodes comments and copying structure.

Synthesis structure

This structure summarizes all differences between reference Bayesian network and comparison structures.

• black: Arc or edge that exist in the reference and in at least one comparison network

• blue: Arc or edge that do not exist in the reference network but that exist in at least one comparisonnetwork

• red: Arc or edge that exist in the reference network but that do not appear in any comparison network

An arc is displayed with an arrow, an edge is a simple line and the V-Structure is displayed as a portionof circle.

Arcs, edges and V-Structures thickness depends on the frequency of the concerned object: the thicker,the higher its frequency.

Hints appear when the mouse is moved over an arc, an edge or a V_Structure, the hint contains thename of the object, if it has been added, removed of if it is constant with regards to reference structure.It also contains the frequencies:

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The synthesis structure can be printed or saved in a spare image file by clicking the buttons.

Reference structure

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The reference structure is the initial Bayesian network (or its equivalence class) that is used for thecomparison basis. The V-Structures of the reference are also displayed.

Comparison structures

Each network obtained from the cross validation is displayed and numerated from zero, the V_Structuresof the network or its equivalence class are also displayed.

Since a comparison structure can represent several identical networks, the total number of networksincluded in this manner is indicated in the picture caption.The frequency equals the number of networksrepresented by the comparison structure divided by the total number of networks produced through thecross validation.

9.1.2. Comparison of Joint Probabilities

This tool is used to compare the joint probability distributions from two different files. These files havebeen previously generated by the Batch Joint Probability keeping only the computed joint probab-ility in the destination file.

This analysis is similar to the Global Network Performance but on the joint probabilities present in theinput files.

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For each panel, the mean, standard deviation, minimum, maximum and computed row numbers are in-dicated below the chart.

In a first time, each file of joint probabilities is analyzed separately:

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Second file:

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Comparison :

The Kolmogorov-Smirnov Test is computed to mesure the distribution adequacy between the twosamples. this test is present in the comparison panels only. It compares the two distributions of log-likelihoods. The values Z, D and the corresponding p-value are displayed.

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9.2. Arc Confidence

The menu item Tools>Cross validation>Arc confidence allows computing a frequency value that measureshow robust is each arc. The network needs a database and the validation mode must be activated.

For this purpose, the Jackknife method is used. It consists at splitting the database into k samples ofequal size but before this step, the database is shuffled in order to avoid bias due to a sorted database.In this context, k-1 samples are used in order to learn k networks while the k sample is not used.

If the initial database is stratified then the generated database wil be stratified in the same way.

If the initial network has a coefficient of structural complexity not equal to 1 then a new coefficient iscomputed, for the new networks, in the following way: new SC = initial SC * new learning weight /initial learning weight. the learning weight is the sum of the weights of the database.

Parameters

In the following window, the learning algorithm shall be selected, as well as the number of data samplesto be generated.

The window displays sample size depending on the size of the database and the number of samples.The samples are chosen randomly in order to avoid the errors that can occur when the database issorted.

In the output directory can be saved all networks and databases learnt during Jackknife process.

Depending on the chosen learning algorithm, a dialog box displays specific settings:

Analysis report

Once the networks have been learnt on each data sample, the following report is displayed:

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It is composed of four parts:

1. The learning context: Reminds the learning method and the number of data samples. It also indicatesthe structural complexity coefficient used (it is the same as the one used in the initial network).

2. Arcs confidence analysis: Lists of arcs grouped by three colored types

• Black: the arcs that exist both in the reference structure and the networks from the samples.

• Arc frequency represents how often the arc appeared with the same orientation as in the samplenetworks.

• Inverted arc frequency represents how often the arc appeared with the reverse orientation as inthe sample networks.

• Edges frequency represents how often the arc appeared without any orientation as in the samplenetworks (the equivalence class of the learnt networks is used).

• Total frequency is the sum of all previous ones. It indicates the overall strength between thevariables.

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• Blue: the arcs that exist in at least one sample network but that do not exist in the reference network.In this case, the frequencies are displayed with a negative value. The reference orientation of arcis arbitrarily given by the first arc found in the first sample network.

• Arcs frequency represents how often this arc appeared with the same orientation as the first.

• Inverted arc frequency represents how often this arc appeared with the reverse orientationcompared with the first.

• Edge frequency represents how often the arc appeared without any orientation (equivalenceclass).

• Total frequency is the sum of all previous ones. It indicates the overall strength of a relationshipthat does not exist in the reference network.

• Red: arcs that exist in the reference structure but that have never been found in any learnt sample.

3. V-Structures confidence analysis: Lists of V-Structures grouped by three colored types:

• Black: V-Structures that exist both in the reference structure and the networks from the samples.

• Blue: V-Structures that do not exist in the reference structure but that appeared in at least once ina sample network. Frequencies are displayed with a negative value.

• Red:V-Structures that exist in the reference network but that never appeared in any sample network.

4. Comparison structure array: It summarizes all learnt networks from the samples. When identicalstructures exist, they are gathered.

• First column is the structure identifier

• The second column is the number of identical structures learnt.

• The third column represent the frequency of the whole structure: it is the number of times the currentstructure appears divided by the total number of structures.

• The last column indicates whether the reference structure is included or not in the current structure.

The report can be saved in a HTML format file. It can also be printed. Two other options exist: displayinggraphs and extracting the network.

Graphs

The Graphs button from the report allows displaying the graphical structure comparator. With thistool, data contained in reports can be viewed and interpreted easily.

Extracting the network

The Network extraction button from the report displays network extraction tool. This tool allowsbuilding a network from any structure depending on arcs frequency thresholds.

9.2.1. Data Perturbation

The menu item Tools>Cross validation>data Perturbation allows avoiding the local minima of the network'sstructure in which the network can be trapped. The network needs a database and the validation modemust be activated.

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The BayesiaLab's structural learning algorithms are based on heuristic search.Then, they can be trappedinto local minima. As they are based on different heuristics, those local minima can be different. Applyingevery algorithms and choosing the one with the lowest score represents the first solution to optimize theobtained network.This data perturbation tool provides another solution consisting in adding noise to theweights associated to each line of the database in order to try escaping from local minima.

A noise is generated by using a Gaussian law, with 0 mean and the standard deviation set by the user.The selected learning algorithm is applied on this perturbed database and the score of the final structureis computed by using the original weights. The decay factor is applied after each iteration to reduce thestandard deviation.

Parameters

Simply select the learning algorithm we want to use, and indicate the initial standard deviation, the decayfactor and the number of tests to perform in the following dialog box:

An output directory can be specified where all networks learnt will be saved.


Analysis report

Once the networks have been learnt, the following report is displayed:

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This report is similar to the Arc Confidence except for the last table where the column indicating theStructure's Mean Score has been added.

The report can be saved in a HTML format file. It can also be printed. Two other options exist: displayinggraphs and extracting the network.

Graphs




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9.2.2. Targeted Cross Validation

The menu Tools>Cross Validation>Targeted allows performing a targeted cross validation based on thecurrent network. The requirements are (1) the network must have associated data, (2) the validationmode must be activated and (3) the network must have a target variable.

For targeted cross validation, the k-Folds method is used. It consists at splitting the database into k parts(the folds) and using k - 1 folds for learning a set of k networks but before this step, the database isshuffled in order to avoid bias due to a sorted database. For each network, the last k-th fold is used fortesting the network and measuring its predictive performance. For each network learnt, the continuousvariables are re-discretized according to the variable distribution in the fold. The discretization methodis the same as the one used for the reference network. On the contrary, initial aggregations are kept.

If the initial database is stratified then the generated database wil be stratified in the same way.

If the initial network has a coefficient of structural complexity not equal to 1 then a new coefficient iscomputed, for the new networks, in the following way: new SC = initial SC * new learning weight /initial learning weight. the learning weight is the sum of the weights of the database.

On this basis, the networks structures are learnt using the chosen algorithm, and the network's targetednetwork performance is computed.

Parameters

The learning algorithm and the number of folds shall be chosen from this dialog box:

The sample size is calculated depending on the size of the database and the number of folds. Thesamples are chosen randomly in order to avoid the errors that can occur when the database is sorted.

An output directory can be specified where all intermediate networks learnt from the folds shall be savedwith their corresponding database.

Results

Network's targeted performance is displayed in this window:

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The first panel "results synthesis" displays the global results computed on all the samples for:

• global precision

• R: Pearson's coefficient

• R2: squared Pearson's coefficient

• relative Gini value

• relative Lift value

• confusion matrices : for occurrences, for reliability and for precision

Nodes frequency array indicates how often a node appears in any network built upon a fold (no matterit is directly connected to the target node or not).

The Global report button (in the synthesis panel) displays the cross validation synthesis report.

The tabs contain the targeted performance result of each network learnt on the folds:

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The details about the panel contents can be found in the targeted performance targeted performancereport section.

Global analysis report

Once all the networks are learnt, the following report is generated:

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The report is built on the same template as the global targeted evaluation report, save that it summar-izes all values for each index and each matrix calculated for each fold.

The rest of the report contains the nodes frequencies.

The last part of the report contains structural comparison of reference network with the generated net-works:

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Its contents are the same as arcs confidence analysis.

This report can be saved in a HTML-format file and can also be printed.Two other options exist: displayinggraphs and extracting the network.

Graphs



The Network extraction button from the report displays network extraction tool.This tool allows buildinga network from any structure depending on arcs frequency thresholds.

Saving the values

The Save Values button of the report allows saving into a file the numerical values of the target predictedby each network on its corresponding test set.

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9.2.3. Structural Coefficient Analysis

The menu item Tools>Cross validation>Structural Coefficient Analysis allows computing a frequencyvalue that measures how robust is each arc. The network needs a database and the validation modemust be activated.

Caution

Use only when data is scarce.

For analysing the structural coeficient, the chosen learning algorithm will be tested with different valuesof the structural coefficient in a given interval. At each iteration, the network structure is learned on entiredatabase with a growing structural coefficient.

Parameters

Simply select the learning algorithm we want to use, and indicate the minimum and maximum limits forthe structural coefficient and the number of iterations to perform in the following dialog box:

The structural coefficient can vary from 0 to 150.

Three options are available allowing computing at each iteration:

• Structure/Data Ratio: use it for unsupervised tasks. It is the ratio between the natural structuralcomplexity (with a coefficient to 1) of obtained networks and their data likelihood (with a coefficient to0).

• Target's Precision in %: use it for supervised tasks. A target node is necessary. The precision ofthe target prediction is computed for each obtained network.

• Structure/Target's Precision: use it for supervised taskstaking into account the structure complexityand the precision. A target node is necessary.

The tested structural coefficients will vary from the given minimum to the maximum by step of (maximum- minimum) / number of iterations.

An output directory can be specified where all networks learnt will be saved.

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Analysis report

Once the networks have been learnt on each structural coefficient, the following report is displayed:

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This report is similar to the Arc Confidence except for the last table where the column indicating themaximum structural coefficient of the structure has been added.This indicates, among the coefficientstested, which is the greatest that has obtained this structure.

The report can be saved in a HTML format file. It can also be printed.Three other options exist: displayinggraphs, extracting the network and displaying the curves.

Graphs




Curves

The button Curves of the report allows displaying the curves corresponding to the options chosen inthe parameters. A dialog box allows the user to choose the curve to display:

• Structure/Data Ratio : the structural coefficient can be chosen in the area at the inflection point ofthe curve, just before a strong increase by reading the graph from right to left.

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• Target's Precision in % :

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• Structure/Target's Precision Ratio :

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9.2.4. Network Extraction

A network can directly be extracted from the obtained results from arcs confidence or targeted crossvalidation. This option is available from the corresponding report.

The network extraction button displays this dialog box:

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This tool automatically creates a network in which all arcs present a frequency equal or superior to theindicated threshold. With this operation, only the strongest relationships between variables are kept.The network's conditional probability tables are learnt from initial data.

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9.3. Multi-Quadrant Analysis

This function can be found in the Tools menu. The network must have a database and a target node.This tool allows analysing a network having a variable called "selector" which must be different from thetarget node. for each state of this variable, one of the three available analysis will be performed on thevariables of the network with respect to the target. In this way, it is possible to analyze the behavior ofeach variable with respect to the target for each state of the selector variable and to compare thosebehaviors between them.

The classic use of this tool is when the variable "selector" is a list of products we want to compare witheach other to analyze their strengths and weaknesses relatively to the target variable. In the examplewe use, the variable selector (Product) represents a range of perfumes and the target variable is thePurchase Intent of these products. Other variables that will be analyzed in relation to the target representthe qualities of these perfumes.

The translucent nodes are not taken into account in these analysis.

For each state of the selector, the algorithm will create a network with the same structure as the originalnetwork and with a database containing only the lines corresponding to the current state.The probabilitytables are learned with these new data. Then the selected analysis is performed on each network.

Parameters :

The following panel lets you define the parameters of the analysis.

• Selector Node: you can choose from a drop down list the variable that will be used as selector node.The target node is excluded from this list.

• Analysis: allows choosing the analysis among:

• Mutual Information: compute the conditional mutual information between each variable and thetarget

• Total Effects: compute the total effects of the variables on the target

• Standardized Total Effects: compute the standerdized total effects of the variables on the target

• Linearize Nodes' Values: by checking this option, the values associated with states of nodes arerecomputed and sorted in order to have a positive increasing impact on the value of the target variable.

• Regenerate Values: by checking this option, the values associated with states of continuous nodesare re-computed from the data in each database for each state of the selector variable. If the lineariz-ation is requested, it will be done after the generation of values.

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• Output Directory: allows specifying a directory in which each network corresponding to each stateof the selector will be saved.

Results :

The display of the results takes the form of points positioned on a 2D chart. It is similar to quadrant chartin the correlation with the target node report or in the total effects report.

The points represent the variables. If a node has a color then the point will be displayed in this color.The name of the node is displayed at the right of the point. When moving the mouse over a point, the

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coordinates are displayed in the top panel. The top panel shows the number of points displayed as wellas the evidence context. It is possible to zoom in the chart as in the scatter of plots.

The mean value of the nodes is displayed along x-axis and the reult of the chosen analysis is along they-axis.The title of the chart indicates the performed analysios and the current state of the selector node.the states can be selected via the chart's contextual menu.

The chart's contextual menu allows to :

• Display the comment of the nodes instead of their name

• Display the long names of the states

• Display the scales

• Select the state to display by choosing one in the proposed list

• Copy the chart as image or array of points (text or html)

• Print the chart

Actions:

The chart above represents the value of each node according to the chosen state. When we move themouse over a node, other nodes disappear and the values of this node for each state of the selectorare displayed. In the example, the relevant node is "Tasty" for the state 8 of the selector node "Product".Other values of "Tasty" are displayed with the name of the corresponding state next to them.

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When choosing the option Display Scales from the contextual menu, chart displays for each node ascale between the minimum and maximum values among all states of the selector. The mean is alsoindicated by a vertical line. It is therefore possible to easily identify where is the value of the node forthe current state among all other states. So we can identify the possible negative and positive progressmargins for the current product for each of its qualities.

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By hovering the mouse over the point, we obstain, as previously, the different values of the node foreach state in addition to the scale:

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The button Export Variations allows exporting the percentages of negative and positive variations ofeach node in order to use them in other analysis thanks to the mean variation editor.

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10. Dynamic Bayesian networks

Graphical Representation

Even if it is possible to take into account the temporal dimension with a static Bayesian network, by un-rolling the network on the desired number of time steps (i.e. by duplicating the network for each timestep, as illustrated on the screenshot below on 4 time steps), this solution is possible only for a limitednumber of time steps.

Dynamic Bayesian networks provide a representation much more compact for such stochastic dynamicsystems. This compactness is based on the following assumptions:

• The process is Markovian, i.e. the variables of time step t depend of set of variables that belong to alimited set of former time steps (usually only the previous time step t-1, first-order Markovian assump-tion)

• The system is time invariant, i.e. the probability tables do not evolve with respect to time. This lastassumption is partially relaxed in BayesiaLab thanks to the Time variable that makes it possiblemodifying the probability distributions according to the value of the current time step by the means ofthe equations.

For first-order Markovian assumption, it is then possible to represent these systems only with two timeslices. The screenshot below represents the same network as the unrolled network presented above,without any limitation on the number of time steps. The first slice describes the initial network at timestep t0 and the second one describes the temporal transitions t+1.

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The specification of the t+1 slice is carried out by the means of the temporal arcs (red arcs). A temporalarc indicates that the two connected nodes correspond to the same node at two consecutive time steps.The set of nodes that belong to the t+1 slice are then the destination nodes of the temporal arcs, andthe descendants of these destination nodes.

For Markovian assumption of higher order than one, the node of time slice (t+1) are also linked to nodesbelonging to time slices former than time slice t. However, temporal arcs can only be used to link nodesfrom time slice t and (t+1).

The initial slice is particular because its synchronous arcs (connecting nodes that belong to the t0 slice,as for example N0 - > N1 t0 and N0 - > N2 t0 in the example above) are removed after the first temporalinference. We then have the common representation of dynamic Bayesian networks in which nodes ofthe t slice have no parent.

Inference

Inference in the dynamic networks is not as simple as in the case of the static Bayesian networks.BayesiaLab proposes two kinds of inference:

• inference based on a junction tree: exact inference for static networks, but that can return approximateresults in the dynamic case. In some particular cases, as for example, the Valve system illustratedbelow on the left, the inference result is exact because the valves are independent from each other.To get exact results with dependent temporal nodes, it is necessary, on a similar fashion as the oneemployed for Bayesian updating, to qualitatively indicate these dependencies (without modifying theoriginal conditional probability table to keep the possible marginal independence), by simply addingarcs between these dependent nodes, as illustrated below, on the right, with the red marked arcs.

• inference based on Monte Carlo simulations (particle filtering): approximate inference in the static anddynamic case, but the approximation is of the same order in both cases, i.e. the approximation is notrelated to the dependence of the nodes but it’s only due the randomness of the simulation.

Temporal Simulation

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In Validation mode, the toolbar has five new tools:

• reset the network (the synchronous arcs and the probability tables of the t0 slice are reset). Thenetwork is also reset after the entry of new probability distributions of the temporal father nodesand when switching to Modeling mode.

• time meter indicating the current time step value. This meter is also used to enter the numberof time steps to reach, i.e. the length of the simulation. If this number is lower than the current timestep value, the network is reset. Otherwise, the simulation is carried out from the current time step tothe entered number. The simulation can be stopped by using the red light of the status bar. If atemporal evidence scenario file is associated to the network, a right click on the index textfield dis-plays a list of the evidence sets contained in the file. A click on a line performs the temporal simulationfrom the current index to the specified index, taking into account the corresponding evidences:

• simulate temporal step by temporal step.

• graphical view of the probability evolution of the temporally spied nodes, as illustrated below.

If a temporal evidence scenario file is associated to the network, the evidences corresponding to eachtime step will be taken into account. It is possible to add a set of evidences for the current time step bypressing the button located in the monitor's toolbar.You must know that setting the probability distri-bution of a node will change according to the chosen inference: fixed distribution with exact inferenceor computation of the corresponding likelihoods with approximate inference.

Caution


The temporal chart button displays the following window:

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For each spied state, the mean of the probability over the simulated period appears in the caption. If thenetwork has utility nodes, the mean of the expected value of each utility node appears in the upperright corner, as well as the total of these expected values.

A right click on the graph activates a contextual menu that allows:

• having a relative view of the graph (the Y-axis takes into account the minimal and maximal valuesand not 0 - 100 as it is the case in the default view)

• printing the graph,

• copying the graph. It can be pasted as an image or as a data array into external applications.

Points can also be saved directly into a text file.

10.1. Time variable

The time variable is a parameter variable that represents the time and that can be used in the formulasdescribing probability distributions. This variable is activated by using the contextual menu associatedwith the background of the graph panel. Its value, that is always observed, is a positive integer thatcorresponds to the value of the current time step of the dynamic Bayesian network (the value thatappears in the time meter in Validation mode).

This is not a classical Bayesian network variable. It can be used in the formula of any node if it is activated.The corresponding probability tables don't reference it explicitly. There are only the probability valuesthat depend directly of its value. The graphical indicator located in the status bar of the network'swindow indicates only that it is possible to use this variable:

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During the temporal inference, after each time increment, the probability distributions described by theequations that use this parameter are updated. Note that in Modeling mode, its value is set to zero (theresulting probability tables are then computed by replacing t with zero)

The use of this parameter transforms the network into a dynamic Bayesian network.

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11. Options

• Console: Allows managing the console (open, clear and save as)

• Settings: Allows managing the preferences of BayesiaLab

11.1. Settings

The different settings of BayesiaLab are located in the following dialog box that you can reach throughthe menu Options>Settings:

The left side displays a tree in which you can select the settings you want to display. Each branch ofthe tree can have sub-branches that you can also select.

The right side displays the selected settings. It contains a button Default values that allows to load thedefault values only for the selected settings. The Apply button validates the displayed settings modific-ations only.

The dialog box contains also two buttons: The Accept button validates all the settings that have beenmodified, displayed or not, and closes the dialog box. The Cancel button cancels all the modificationsof the settings, displayed or not, if these ones were not already validated and closes the dialog box.

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General

This item is visible only if your license allows it. It is also not available for Mac OS X.

When an instance of BayesiaLab is already running, if the user wants to open again BayesiaLab orperforms a double-click on a XBL file, the previous instance will be automatically reused. The followingoptions allows managing this behavior:

• Allows opening multiple instances of BayesiaLab: when an instance of BayesiaLab is alreadyrunning, it is possible to open a new instance if the license allows it. Opening a new instance can bedone either by running directly BayesiaLab or by double-clicking on an XBL files for example (dependingon the second option). It works as well with command line on any platform. If the option is unchecked,opened instance will be always reused and the second option will be always checked.

• Reuse opened BayesiaLab when double-clicking on XBL files: when an instance of BayesiaLabis already running, it is possible to reuse it when the user performs a double-click on an XBL file (orby command line). If the first option is checked and this option also, the user will open a new instanceof BayesiaLab if he runs directly the program and he will reuse an already opened instance if hedouble-clicks on a XBL file. It works as well with command line on any platform.

BayesiaLab needs to be rebooted to take changes into account.

Language

Allows choosing the BayesiaLab's language. These languages are available:

1. English

2. Spanish

3. French

4. Japanese

5. Chinese

BayesiaLab needs to be rebooted to take the language modification into account.

Display

Customize the Bayesian networks windows:

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• Font smoothing: the drawing of the font is smoothed

• Display background image: displays or not the background image of the Bayesian networks windows.Images can be changed by using the contextual menu.

• Background color: double-clicking on the colored square allows choosing the color of the Bayesiannetworks windows background.

• Positioning grid spacing: indicates the size in pixels of the grid spacing.

• Default Node Font: indicates the default font used to display the nodes' name for all networks. Thisfont can be modified for each network through the network's contextual menu.

• Default Comment Font: indicates the default font used to display the comments if no font is manuallyspecified in the comment. This font can be modified for each comment in the comment editor.

Console

Customize the console:

• Auto save console: automatically save the content of the console.

• Background color: double-clicking on the colored square allows choosing the color of the consolebackground.

• Text color: double-clicking on the colored square allows choosing the color of the console text.

Options_menus

Customize the menus:

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• Recent network list size: allows specifying the number of recently opened networks you want tokeep in the menu Networks>Recent networks.

• Recent database list size: allows specifying the number of recently opened databases you want tokeep in the menu Data sources>Recent databases.

• Display Copy Format Choice When Copy: allows us to display, when a table, a graph, monitors,or other, are copied, a dialog box asking in which one of the available format the user wants to copy.According to the copied object, it is possible to copy as plain text, HTML or image. Under Windows,it is possible to uncheck this option, since the clipboard system allows us to copy several format atthe same time, the choice of the format being done during pasting.

• Copy as Images with Transparent Background: when a copy as image is done on a network ormonitors (for example), the background of the image is transparent instead of being white. Sometimes,on some software like MS Word, transparent background is interpreted as black. In these cases, youcan choose to uncheck this option or to perform a copy on another software that supports transparencydirectly (like MS Excel or MS PowerPoint) and copy again the image into the target software.

Menus > Perspectives

Customize the perspectives:

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Perspectives allows the user to configure the different menus of BayesiaLab as he wants. Each menuof the menu bar is present in the column Component and can be set visible or not if the user doesn'tneed it. This can be done by checking of not the corresponding option in the column named Visible. Itis also possible to configure the keyboad shortcut for each menu item. The column Shortcut shows thecurrent shortcut associated with the menu item. Some of components cannot have their visibilitiesmodified, like Settings and Perspectives for obvious reasons.The last column Count shows how manytimes each action has been done. It is useful to understand how BayesiaLab is used. A special toolallows analyzing these results.

It is possible to edit the shortcut of a menu by selecting the component in the list, for example Target'sOptimization Tree:

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Once selected, the buttons and field in the bottom part become available. After that, you can choosenone, one or several modifiers among Ctrl, Meta for Mac users, Alt, Shift and Alt Graph. Now click onthe field and type the key you want for the shortcut. In our example, we want to create the shortcut Ctrl+ O. So the button Ctrl is pressed and the key O is typed in the text field. The interface indicates thatthis shortcut is already used for the Open menu, so we must change the keystroke by pressing thebutton Alt in order to obtain Ctrl + Alt + O.

To remove a shortcut, select it and click in the text field. Once the focus is on the text field press the key or (not the buttons).

The button Load allows importing a perspective file. The button Save allows exporting the current per-spective into a text file.

To validate all the changes, you must click on the Apply or Accept buttons.

Directories

Customize the user directories:

Allows choosing the directories which will be used for the graphs, the databases, the images and otherfiles (reports, etc). It is possible to use the same directory for all by selecting the convenient option.

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The option fixing the different paths prevents from updating the paths when one of them is changed atthe opening or saving of files.

Editing

Customize network editing:

• Maximum state number allowed: allows specifying the maximum number of states allowed for anode. This number is used in the database import and in the node editing.

• Warn when the Data of a Deleted Node will be Lost: displays a warning when the user wants todelete a node having data associated with it which will be lost.

• Warn when CPTs are lost when inverting arc: displays a warning when inverting an arc, indicatingthat the content of the conditional probability table will be lost.

• Warn when the size of a CPT is too big: checking this option activates the beneath option Size al-lowed before warning that makes it possible to specify the size of the CPTs that is allowed beforeindicating the overflow. This option allows avoiding the creation of too big CPTs that decrease per-formances and that use too much memory.

• Automatically back to selection mode: comes back to selection mode after doing any action (creationor deletion of a node or an arc).

Data

• Import exact values of the continuous variables: allows choosing if the continuous values of thediscretized variables are loaded in memory or not.These values are used by the Graph module, andalso to compute the mean and standard-deviation in the monitors. Warning: this option can use a lotof memory.

• Save Database with Network: Allows the user to save the database associated to a network in thesame file in order to be able to reopen them together. When a network is opened with an associateddatabase, an option in the file chooser allows the database to be loaded or not.

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• Save Evidence Scenario File xith Network: Allows the user to save the evidence scenario fileassociated to a network in the same file in order to be able to reopen them together. When a networkis opened with an evidence scenario file, an option in the file chooser allows the evidence scenariofile to be loaded or not.

Data > Import & Association

• Default completion: completion mode of missing values used by default during the import process.

• Default discretization: discretization mode used by default during the import process.

• Default interval number: number of intervals used by default for the discretization during the importprocess.

• Minimum Interval in Database Size Percent for KMeans Discretization: indicates the minimumpopulation of an interval that is needed to keep it during KMeans discretization when importing.

• KMeans Filter Size in Percentage: gathers data into packets of the given size in order to removethe effect of the outliers (abnormal values). A size of 0 deactivates the filter.

• Set State Value to Interval Mean at Import: for the continuous nodes, allows setting as value asso-ciated with the state the corresponding interval's mean at import. It is the same for a variable addedduring associating.

• Set State Value to Interval Mean at Associate: for the continuous nodes, allows setting as valueassociated with the state the corresponding interval's mean at associate time. The added variablesfollow the same option as with import.

• Weight normalization: if the database has a weight column, two alternatives are available:

• no normalization: the weight of each line is the one that is in the database;

• normalization: the weight of each line is normalized to get a sum over the weights equal to thenumber of lines of the database multiplied by the user defined normalization factor.

Data > Import & Association > Missing and Filtered Values

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• Default Missing Values: Defines the default list of values that will be considered as missing valuesduring importing and associating. During importing or associating, it is obviously possible to modifythis list.

• Default Filtered Values: Defines the default list of values that will be considered as filtered valuesduring importing and associating. During importing or associating, it is obviously possible to modifythis list.

Data > Save Format

Customize the format used to save data. It allows to choose the column separator and to define if thepoint is used or not to indicate the end of the line.

• It is possible to choose the column separator.

• It is also possible to choose the comma or the dot as decimal separator symbol.

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• It is possible to define if the point is used or not to indicate the end of the line.

• The output file encoding can be changed in the combo box according to the used character sets.

• When the chosen encoding is UTF, it is possible to write or not the Byte Order Mask at the beginningof the file.

Reporting

Customize reports generation:

• Display the node's color in the cell's background: if the node has a color associated with it, thiscolor will be used as the background color of the cells where the node's name is.

• Display node comments in tables: adds a column in the reports containing the comment of eachnode.

• Display node comments in tool tips: this option allows displaying the comments associated witheach node into a tool tip by moving the mouse over the node. However, in some cases, if you needto open the saved HTML file with external software, such as Excel for example, it can be necessaryto disable this option.

>Automatic Layout

Customize automatic layout:

Allows choosing the automatic layout algorithm associated with the shortcut between:

• Dynamic layout algorithm

• Symmetric layout algorithm

Automatic Layout > Symmetric Layout

Customize symmetric layout:

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• Multi-level: hierarchical algorithm where the initial network is recursively decomposed into sub net-works. The symmetric algorithm is then applied in an ascending fashion on each of the obtained net-works.

• Repulsion factor: indicates the repulsion force between the nodes.

• Optimization factor: optimize the layout precision.

Automatic Layout > Genetic Algorithm

Customize layout genetic algorithm:

• Number of races: number of distinct populations used in the genetic algorithm.

• Size of the populations: number of solutions for each race.

• Individual mutation rate: mutation rate associated with each solution.

• Gene mutation rate: if the individual is mutating, each gene can mutate with this mutation rate.

• Selection rate: rate corresponding to the solutions that will be replaced by new solutions generatedby crossover.

Automatic Layout > Genetic Algorithm > Evaluation Function

Customize the evaluation function of the genetic algorithm layout that allows indicating the weight asso-ciated with each aspect of the evaluation function:

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• Family relationships weight: importance attached to have child nodes below their parents.

• Angle weight: importance attached to the vertical arc.

• Node overlapping weight: importance attached to prevent the node overlapping.

• Arc length weight: importance attached to reduction of the difference between the arc size and thesize indicated by the slider.

• Intersection weight: importance attached to prevent of the arc intersections.

• Class weight: importance attached to reduce the distance between nodes of the same class.

Analysis

Customize analysis

Analysis > Variable Clustering

Customize variable clustering:

• Maximum Cluster Size: indicate the maximum number of clusters automatically chosen by the al-gorithm.

• Stop Threshold: indicates the threshold corresponding to the maximum KL weight a cluster can haveto be kept.

Inference

Customize inference:

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• Display probability variations: arrows are displayed on the monitors in order to indicate the differencebetween the previous marginal probability of a node and its current one.

Inference > Exact Inference

Customize exact inference:

• Network complexity reduction rate: indicates the threshold from which the complexity reductionalgorithm must act if the network is too complex to allow performing exact inference. A weak reductionrate will let a network strongly connected and the inference should be more time consuming. It will bethe opposite with a high rate. In all cases, if the algorithm needs to be run, the user will be informed.

Inference > Approximate Inference

Customize approximate inference:

• Likelihood Weighting iteration number: indicates the number of samples used to compute theprobabilities. More this number is high, more the computed probabilities are precise but more thecomputing time is long.

Learning

Customize learning:

• Repaint while learning: displays the intermediate states of Bayesian networks during the learningprocess.

• Smoothed probability estimation: the conditional probability tables can be estimated with asmoothing parameter.This parameter corresponds to the initial virtual occurrences that are generatedin agreement with the probability law described by the fully unconnected Bayesian network with onlyuniform probability distributions, i.e. each variable is independent and all the values of the variablesare equiprobable.

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• Temporal threshold to estimate missing values: defines the maximum duration between twomissing values estimation during structural learning. Beyond this threshold, a dialog box allows tostop learning. This option is very useful to learn a Bayesian network with a structure that can be sub-optimal but that allows to carry out exact inference in a time that is proportional to the defined threshold(the time between two learning time steps corresponds to the inference of the missing values with thecurrent network).

• Maximum number of iterations for the completion process: defines the number of maximal iterationsfor the algorithms of missing value estimation. The higher this value is, the better the probabilityestimation is. Caution, the time necessary to estimate the probabilities also increases proportionallyto this parameter.

Learning > Association Discovery

Customize association discovery:

• Taboo list size: defines the forbidden states list size for the Taboo algorithm.

• Taboo Order list size: defines the forbidden states list size for the Taboo Order algorithm.

Learning > Data Clustering

Customize data clustering:

• Maximum Drift: indicates the maximum difference between the clusters probabilities during learningand those obtained after missing value completion, i.e. between the theoretical distribution duringlearning and the effective distribution after imputation over the learning data set.

• Minimum Cluster Purity in Percentage: defines the minimum allowed purity for a cluster to be kept.

• Minimum Cluster Size in Percentage: defines the minimum allowed size for a cluster to be kept.

Learning > Policies of Dynamic Networks

Customize policies of dynamic networks:

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• Discount factor: this factor is used to mathematically bind the sum of the reinforcements that will bereceived over an unlimited horizon. It is also used to weight the future with respect to the present (0<= factor <= 1). 0 reduces the action quality value to the expected direct reinforcement whereas 1implies that the quality value is the total sum of all the reinforcements received over the (finite) horizon.

• Adaptive learning rate: allows the automatic adjustment of the learning rates during learning. Ifvarious consecutive modifications have the same direction, the corresponding rate is increased, oth-erwise, it is reduced. This option can allow speeding up the convergence of the learning algorithm.

• Learning rate: rate used in the update rule (0 <= rate <= 1). 0 prevents learning while 1 implies thatthe error term is fully impacted in the quality value.

• Initial exploration rate: rate used to balance Exploration and Exploitation during learning. Explorationmeans that actions are chosen randomly, whereas Exploitation means that actions are chosen accordingto their quality value (0 <= rate <= 1). 0 prevents exploring while 1 implies a fully random policy. Thisrate is automatically decreased during learning to converge toward a pure exploitation phase.

Statistical Tools

Customize the statistical tools:

• Used Independence Test: Allows the user to choose between the Chi and the G-test as independencetest used in mosaic analysis, correlation with the target node report (network and data), totaleffects on the target (network and data) and relationship analysis report (data).

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12. Help

• Help: to display this help.

• Context Help: changes the mouse cursor into a ? and then the user can click on the component hewants help on.

• Feedback Form: online form for evaluating BayesiaLab.

• Use Analysis: allows analysing the use of BayesiaLab.

• About BayesiaLab: displays information on the current version of BayesiaLab.

12.1. Analysis of the use of BayesiaLab

This analysis can be accessed by the menu Help > Use Analysis.

With the registration of the use of each menu of the BayesiaLab's menu bar (see Perspectives), it ispossible to make graphical analysis of the use of BayesiaLab's tools.

The window contains in its right hand side the tree of BayesiaLab's menus. Each item can be selectedand the chart of use appears in the right side as a pie chart. Pie charts can be displayed under two formsthat can be selected by the options on the right:

• Use percentage indicates the number of used functions and the number of never used functions.

• Detailed use indicates the number of times each function was used.

The following figure shows the overall use of BayesiaLab, i.e. the number of functions used (red) andthe number of functions never used (green). Just move the mouse pointer to display a tooltip informationcorresponding to the specified area.

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When you select a menu or submenu in the tree on the left, the graph shows, then, only the use of theselected menu and its submenus. In the following figure the Analysis menu is selected:

To see the detailed chart, simply press the button Display Detailed Use which displays a window con-taining a larger as well as the detail of the use on the right hand side.

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When you click on the second option, the chart displays the number of times each function was used,according to the menu selected in the tree:

To see the detailed chart, simply press the button Display Detailed Use. The right part shows for eachsector the number and percentage of use compared to the sum of all uses.

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The button Display Table opens a new window containing the table all BayesiaLab's menus with theirname, their icon, their visibility, their shortcut, and their number of uses. When a row is selected,pressing on the button help displays the help corresponding to the function, if it exists.

the table is sortable by clicking on each column's header.

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Chapter IV.ToolbarsBayesiaLab proposes several toolbars according to the mode in which the network is and also to theoperations applied. The tools of the bar are valid or not according to the state of the graph window.

Network toolbar

Create a new graph window

Open a Bayesian network (in a new graph window)

Save a graph

Print a graph

Edit toolbar

Cut (modeling mode)

Copy

Paste (a right-click before pasting allows specifying where to paste) (modeling mode)

Undo the last possible action

Redo the last undone action

Find

View toolbar

Zoom in

Zoom out

Default zoom

Resize and center the Bayesian network on the current window

Rotate left the graph around the selected node or the center of the graph if there is no selected node

Rotate right the graph around the selected node or the center of the graph if there is no selected node

Display toolbar

Displays or hide the node comments

Display or hide the arc comments

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Display or hide the color tags of nodes

Display or hide the color tags of arcs

Display or hide the images associated with the nodes

Hide or display the comment indicators of nodes and arcs

Display or hide the orientation of the arcs (validation mode)

Creation toolbar

Selection mode

Node creation mode (modeling mode)

Constraint node creation mode (modeling mode)

Utility node creation mode (modeling mode)

Decision node creation mode (modeling mode)

Arc creation mode (modeling mode)

Deletion mode (modeling mode)

Monitors toolbar (validation mode)

Zoom in monitors

Zoom out monitors

Default monitor zoom

Remove all the observations

Remove all the monitors

Remove all probability shifts

Referencing of the probability shifts

Display the maximum probability shifts

Add the current set of evidences to the current evidence scenario file

Temporal inference toolbar (validation mode + temporal variable or tem-poral arc)

Reinitialize the temporal variable to 0

Increase the temporal variable by 1

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Display the graphic representing the evolution of the temporally spied nodes

Temporal inference and dynamic learning of policies toolbar (validationmode + temporal variable or temporal arc + decision node)

Deactivate the exploration

Activate the exploration (testing some random actions) during the temporal simulation

No learning of the state/action qualities during the temporal simulation

Learning of the state/action qualities during the temporal simulation

Adaptative questionnaire toolbar (validation mode + adaptive question-naire)

Reinitialize the entire observations

Stop adaptive questionnaire

Interactive inference toolbar (validation mode + interactive inference)

Go back to the first case of the database (index 0)

Go back to the previous case

Go to the next case

Go up to the last case

Stop the interactive inference

Interactive updating toolbar (validation mode + interactive updating)

Go back to the first case of the database (index 0)

Go back to the previous case

Go to the next case

Validate the current updating

Stop the interactive updating

Arc force analysis toolbar (validation mode + arc force)

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Go back to the previous threshold

Go to the next threshold

Store the current arc forces in the arc comments

Stop the arc force analysis

Arc's mutual information analysis toolbar (validation mode + arc's mutualinformation)

Go back to the previous threshold

Go to the next threshold

Store the current information in the arc comments

Stop the arc's mutual information analysis

Pearson's correlation analysis toolbar (validation mode + Pearson'scorrelation)

Go back to the previous threshold according to the selected correlation

Go to the next threshold according to the selected correlation

Displays only arcs having a negative correlation greater than the given threshold in absolute value

Displays only arcs having a correlation greater than the given threshold in absolute value

Displays only arcs having a positive correlation greater than the given threshold

Store the current Pearson's correlations in the arc comments as well as the associated color

Stop the Pearson's correlation analysis

Node force analysis toolbar (validation mode + node force)

Go back to the previous threshold according to the selected force

Go to the next threshold according to the selected force

Computes only the entering force of the nodes and displays if greater than the given threshold

Computes the global force of the nodes and displays if greater than the given threshold

Computes only the outing force of the nodes and displays if greater than the given threshold

Stop the node force analysis

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Variable clustering toolbar (validation mode + variable clustering)

Displays the current clustering as a dendrogram

Validate the current clustering

Stop the variable clustering

Correlation with the target node toolbar (validation mode + correlationwith the target node)

Stop the correlation with the target node analysis

Correlation with a state of the target toolbar (validation mode + correl-ation with a state of the target node)

Stop the correlation with a state of the target node analysis

Neighborhood analysis toolbar (validation mode + neighborhood analysis)

Combo box to choose the kind of neighborhood Field to modify the neighborhood depth

Stop the neighborhood analysis

Most probable explanation toolbar (validation mode + most probableexplanation)

Stop the most probable explanation

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Chapter V. SearchSearching nodes

The thumbnail Nodes displays the node search user interface. The editable combo box allows enteringthe name of the node or of its class that we are searching. We can use also the special characters *and ?:

• The character * represents a series of 0 to n unspecified characters.

• The character ? represents exactly one unspecified character.

The check box "Case sensitive" means that the capital and small letters will be interpreted as is. Thesearch options allow searching among the nodes only, the classes only or both of them.

Examples:

• if we want to find all the nodes beginning by "Comb", we will enter the following search: "Comb*"(without the quotes)

• if we want to find all the nodes containing the letters "A" and "B" separated by a single character, wewill enter the following search : "*A?B*" (without the quotes)

Once the search is done, the list of the found nodes and the number of nodes are displayed. By selectinga node in the list, this one begins to blink in the graph window. If the window is closed, the current selectionremains displayed.

Searching arcs

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The thumbnail Arcs displays the arc search user interface. This search is done from the name of theextremity nodes and the orientation of the arc. The user interface for both nodes is the same as thesearch of a single node. It is possible to specify, as for the nodes, the field of search of each extremity(nodes, classes or both of them).There are three buttons to indicate the orientation of the arcs we wantto find.

Example:

• if we want to find all the arcs that the end node starts with "Comb", we will enter the following search:"Comb*" (without quotes) for the second node, we will choose the convenient orientation andwe will enter "*" for the first node.

• if you want to add also the arcs that the start node begins by "Comb" simply press on the button .

Once the search is done, the list of the found arcs and the number of arcs are displayed. By selectingan arc in the list, this one begins to blink in the graph window. If the window is closed, the current selectionremains displayed.

Searching monitors

The thumbnail Monitors displays the monitor search user interface. Obviously, you must be in validationmode and having monitored nodes. The editable combo box allows entering the name of the node orof its class that we are searching. We can use also the special characters * and ?:

• The character * represents a series of 0 to n unspecified characters.

• The character ? represents exactly one unspecified character.

The check box "Case sensitive" means that the capital and small letters will be interpreted as is. Thesearch options allow searching among the nodes only, the classes only or both of them.

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Search

Examples:

• if we want to find all the monitors of nodes beginning by "Cap", we will enter the following search:"Cap*" (without the quotes)

• if we want to find all the monitors of nodes containing the letters "A" and "B" separated by a singlecharacter, we will enter the following search : "*A?B*" (without the quotes)

Once the search is done, the list of the found monitors and the number of monitors are displayed. Byselecting a monitor in the list, this one begins to blink in the monitor windows. If the window is closed,the current selection remains displayed.

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Chapter VI. ConsoleThe console is the place of the not preemptive messages of BayesiaLab to the user. It allows visualizingfor example precise values during learning, inference, etc.

As the console is editable, it is possible to insert messages in these results (thanks to the zone of textin the top of the console window). It can be saved and cleared.

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Documents

dimensional

local structural

initialization

local structural

avoid bias

exe program

exportthe

importthe