An Overview of Bayesian Network-based Retrieval Models Juan Manuel Fernández Luna Departamento de Informática Universidad de Jaén [email protected] Department.

AnAn Overview of Overview of Bayesian Network-Bayesian Network-

basedbasedRetrieval ModelsRetrieval Models

Juan Manuel FernándezJuan Manuel Fernández LunaLunaDepartamento de Informática

Universidad de Jaén [email protected]

Department of Computing Science, University of Glasgow

October, 21th - 2002

Bayesian Network-based Retrieval Models

2

Layout

Introduction Introduction to Belief Networks Bayesian Network-based IR Models

• Inference Network Model• Belief Network Model• Bayesian Network Retrieval Model

Relevance Feedback Other applications Bibliography


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Introduction

1. Query and document characterizations are incomplete.

2. The query is a vague description of the users´ information need.

3. Computing relevance degree: 1 and 2 +A) different representations that a concept may have, B) these concepts are not independent among them.

Information Retrieval Uncertain process


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Introduction

Probabilistic models tried to overcome these problems…

Researchers focused their attention on Belief networks in order to apply them to IR because:

They show a high performance in actual problems characterised by uncertainty.


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Introduction to Belief Networks

Graphical models able to represent and efficiently manipulate n-dimensional probability distributions.

The knowledge obtained from a problem is encoded in a Belief network by means of the quantitative and qualitative componets:


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• Qualitative part: Directed Acyclic Graph.G=(V,E):

1.V (Nodes) Random variables, and2.E (Arcs) (In)dependence relationships.


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• Quantitative part A set of conditional distributions:

1. Drawn from the graph structure, 2. representing the strength of the relationships,3. stored in each node.

Belief Network Belief Network Bayesian Network Bayesian Network

(Conditional probability distributions)


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Taking into account these (in)dependences, the joint probability distribution could be restored from the network:

n

iiin XPaXPXXXP

121 ))(|(),...,,(

Pa(Xi) being the set of parents of the variable Xi.

This previous expression implies an important saving in the storage space.


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Construction:– Manual, using an expert´s knowledge.– Automatic, by means of a learning algorithm.

Inference:Given a set of evidences, E, to obtain the probability with which a variable can take a certain value.

p(S=T | W=T)=0.430, p(R=T| W=T)= 0.708


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Bayesian Network-based IR Models

•Inference Network Model

•Belief Network Model

•Peter Bruza´s Index Belief Expressions

•Maria Indrawan et al.´s Model

•Bayesian Network Retrieval Model


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d1 d2 dj-1 dj

q1 q2

inn

r1 r2 r3 rm

Link Matrices

Inference:

Instantiating each document, dj, and computing p(inn | dj).

Inference Network Model


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Belief Network Model

d1 d2 dj-1 dj

Q

t1 t2 t3 tm

)()|()|()|( 1 pQpdpQdp jj

2M assigments unfeasible

Probabilities are defined in such a way that only one configuration is evaluated


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Bayesian Network Retrieval Model

1. There are strong relationships among a document and the terms that index it.

2. Document relationships are only present by means of the terms that index them.

3. Documents are conditional independent given the terms by which they were indexed.

Guidelines to build the BNR Model:


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Term Subnetwork

Document

Subnetwork

Ti {¬ti, ti}

Dj {¬dj, dj}


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All the terms are independent among them:

Simple Bayesian Network Retrieval Model

T1 T2 T3 T4 T5 T6

Term Subnetwork

D1 D2 D3 D4Document Subnetwork


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Probability Distributions:• Term nodes: p(tj)=1/M, p(¬tj)=1-p(tj)

• Document nodes: p(Dj | Pa(Dj)), Dj

But... If a document has been indexed by 30 terms, we need to estimate and store 230 probabilities.

Problem!!!!Problem!!!!


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Solution:Probability functions

)(

))(|(

jj

ji

Dpat

DTijjj wDpaDp

10 ji DT

ijij wandwwhere

pa(Dj) being a configuration of the parents of Dj.


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Retrieval:1. Instantiate TQ Q to Relevant.2. Run a propagation algorithm in the network.3. Rank the documents according p(dj | Q), Dj

Problem:Great amount of nodes and existing cycles in the graph

General purpose propagation algorithms can´t be applied due to efficiency considerations.


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Solution: Taking advantage of:

• The kind of probability function used, and• The topology.

Propagation is substituted by

Evaluation of the probability function in each document node


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Result: An efficient and exact propagation.

)|()|( QtpwQdp iDT

ijj

ji

Including Query term frequencies:

])[|()|( iiDT

ijj qfQtpwQdpji


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Removing the term independency restricction: We are interested in representing the main

relationships among terms in the collection.

Term subnetwork Polytree

Why?There is a set of efficient learning and propagation algorithms available for this topology.


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T1

T2

T3

T4

T5

T6

Term

Subnetwork

D1 D2 D3 D4

Document

Subnetwork


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Probability distributions:

Marginal Distributions (root term nodes):

)(1)(,1

)( iii tptpM

tp

(M being the number of terms in the collection)


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Conditional Distributions (document nodes):

Probability functions

))(,())(()(

))(,())(|(

iiii

iiii

TpatnTpantn

TpatnTpatp

))(|(1))(|( iiii TpatpTpatp

Conditional Distributions (term nodes with parents):

(based on Jaccard´s coefficient)


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Retrieval:

TqQ Relevant

p(dj|Q)??

But... Due to the complexity of the whole network we can not run an exact propagation algorithm.

Solution:

PROPAGATION + EVALUATION


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Propagation:

Running the exact Pearl´s propagation algorithm in the polytree (term subnetwork), p(ti|Q), Ti, are computed.

Evaluation:

Evaluation of a probability function in the Document Subnetwork, computing p(dj|Q), Dj, incorporating p(ti|Q).


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Given a document, Dj:

1. Compute p(dj|di), Di.

2. Select those documents with greatest probability of relevance with respect to Dj.

3. Link Dj with all these documents.

Adding document relationships


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But... Instead of linking the documents in the document subnetwork...

Term Subnetwork

D2 D3 D4 D5 D6 D7D1

D`2 D`3 D´4 D´5 D´6 D´7D`1


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1. We don´t have to restimate probability distributions in the document nodes.

2. Propagation: Evaluation of a probability function in the second document layer Efficiency.

Advantages of this topology:


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1. Compute p(dj|Q), Dj

(1st document layer)

2. Compute p(d´j|Q), D´j

(2nd document layer)

)´(

)|()|(1

)|´(ji DPaD

iijj

j QdpddpS

Qdp

Where Sj is a normalising constant

Retrieval?


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Reducing the propagation time in the Term Subnetwork:

1. Representing only the best relationships among terms.

2. Modifying Pearl´s propagation algorithm.

3. Changing the Term subnetwork topology.


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1. Representing only the best term relationships1. Representing only the best term relationships

Problems:• Automatically learning the relationships among terms could imply that some relationships are not strong

enough.

Retrieval effectiveness could be damaged

• If the number of terms is very high, the learning stage could be time-consuming.


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Solution: Selection of best terms

Collection Classification algorithm

Non-selected terms Selected terms

Polytree learning


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Advantages:-Reduction of learning time

-Representation of the best relationships among terms

-Faster propagation.


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• Classification algorithm: K-means, with Euclidean distance

• Objects: Terms

• Attributes: Term discrimination value (tdv) Inverse Document Frequency (idf)

• Classes: Good terms: higher tdv, and medium-high idf. Rest of the terms.


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2. Modifying Pearl´s algorithm.2. Modifying Pearl´s algorithm.

In large polytrees, the belief of a great number of terms, those furthest from query terms, will not be updated after propagating.

So...Why is the propagation algorithm still running?


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Radial Propagation

r=2


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Linear Propagation


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3. Changing the Term Subnetwork topology.3. Changing the Term Subnetwork topology.

In certain cases, the polytree topology of the Term subnetwork, even using the term selection approach, could not be very appropriate.

An alternative topology:

Two term layers1. Preserving accuracy of term relationships represented in

the graph.

2. Providing an efficient inference mechanism.


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Document Subnetwork

T´2 T´3 T´4 T´5 T´6 T´7T´1

T2 T3 T4 T5 T6 T7T1


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Relationships ara captured using the coocurrences among terms.

The probability of relevance in the second term layer is computed by means of:

)´|()|()(´

QtpvQtp iTPaTijj

ji


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Relevance Feedback in B.N. Models

Inference and Belief Network Models:• Modifying link matrices and adding new links (and also

new document nodes in the second).

Bayesian Network Model:• Inclusion of new evidences from the inspection of the

document ranking using partial evidences.

• (Advantage: neither graph structure modification nor probability matrix re-estimation).


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Other applications:

Indexing Hypertext User profiling WWW Structured documents Image retrieval Document classification Filtering


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Bibliography

• Bruza, P. & van de Gaag, L.C. (1996). Index Expression Belief Network for Information Disclosure. International Journal of Expert Systems. 7(2), 107-138.

• de Campos, L.M.; Fernández-Luna, J.M. & Huete, J.F. (2000). Building Bayesian network-based information retrieval systems. Proc. of the 2nd LUMIS Workshop. 543-550.

• de Campos, L.M.; Fernández-Luna, J.M. & Huete, J.F. (2001). Relevance Feedback in the Bayesian Network Retrieval Model: An Approach Based on Term Instantiation. Lecture Notes in Computer Science. 2189. 13 – 23.

• de Campos, L.M.; Fernández-Luna, J.M. & Huete, J.F. (2001). Document Instantiation for relevance feedback in the Bayesian Network Retrieval model. Proceedings of the SIGIR’01 Workshop on Mathematical and Formal Models in Information Retrieval. 10-18

• de Campos, L.M.; Fernández-Luna, J.M. & Huete, J.F. (2002). A layered Bayesian Network Model for Document Retrieval. Proceedings of the ECIR’2002 Colloquium. Lecture notes in Computer Science, 2291, 169 – 182.


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Bibliography

• Luis M. de Campos, Juan M. Fernández-Luna, Juan F. Huete. Reducing term to term relationships in an extended Bayesian network retrieval model. Proceedings of the Ninth International IPMU Conference (Information Processing and Mangement of Uncertainty in Knowledge-based Systems) Conference, Vol. 2, 1195-1202 (ISBN Vol. 2: 2-9516453-2-5), 2002. ESIA – Université de Savoie (Editor).

• Luis M. de Campos, Juan M. Fernández-Luna, Juan F. Huete. Two terms layer: An alternative topology for representing term relationships in the Bayesian Network Retrieval Model. Electronic Proceeding of the Seventh Online World Conference on Soft Computing in Industrial Applications (wsc7.ugr.es).

• Luis M. de Campos, Juan M. Fernández-Luna, Juan F. Huete. Reducing Propagation Effort in Large Polytree: An application to Information Retrieval. To appear in Proceedings of the Workshop on Probabilistic and Graphical Models. Cuenca (SPAIN), 2002.

• Crestani, F., Lalmas, M., van Rijsbergen, C.J., Campbell, L. (1998). Is this Document Relevant?… Probably: A Survey of Probabilistic Models in Information Retrieval. Computing Survey. 30(4). 528-552.


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Bibliography

• Fernández-Luna, J.M. (2001). Modelos de Recuperación de Información basados en Redes de Creencia. Ph.D. Thesis (in Spanish). University of Granada.

• Frisse M. & Cousins, S.B. (1989). Information Retrieval from Hypertext: Update on the Dynamic Medical Handbook Project. Proceedings of the Hypertext’89 Conference. 199-212.

• Ghazfan , D., Indrawan, M. & Srinivasan, B. (1996). Towards meaningful Bayesian networks. IPMU’96 Conference. 841-846.

• Haines, D. & Croft W.B. (1983). Relevance Feedback and Inference Networks. 20 th ACM-SIGIR Conference. 119-128.

• Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan and Kaufmann. San Mateo, California.

• Reis, I. (2000). Bayesian Networks for Information Retrieval. Ph.D. Thesis. Universidad Federal de Minas Gerais.

• van Rijsbergen, C.J. (1971). Information Retrieval. 2nd Edition. Butter Worths.• van Rijsbergen, C.J., Harper, D.J., & Porter, M.F. (1981). The selection of good search

terms. Information Processing & Management. 17, 77-91.


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Bibliography

• Sahami, M. (1998). Using Machine Learning to Improve Information Access. Ph.D. Thesis. Stanford University.

• Savoy, J. & Desbois, D. (1991). Information Retrieval in Hypertext Systems: An Approach using Bayesian Networks. Electronic Publishing. 42(2), 87-108.

• Turtle, H.R., & Croft, W.B. (1991). Evaluation of an Inference Network-based Retrieval Model. Information Systems. 9(3), 189-224.

• Turtle, H.R., & Croft, W.B. (1997). Uncertainty in Information Systems. In Uncertainty Management in Information System: From needs to solutions. Kluver Academic. 189-224.

• Tzeras K. & Hartman, S. (1993). Automatic Indexing Based on Bayesian Inference Netoworks. 16th ACM-SIGIR Conference. 22-35.

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Thank you very much

An Overview of Bayesian Network-based Retrieval Models Juan Manuel Fernández Luna Departamento de Informática Universidad de Jaén [email protected] Department.

Documents

inference network model

bnr model

d j problem

pd j pad j

belief networks quantitative

belief networks qualitative

belief networks construction

pt j document nodes