Nima Asgharbeygi, Pat Langley, Stephen Bay Nima Asgharbeygi, Pat Langley, Stephen Bay Center for the Study of Language and Information Center for the Study of Language and Information Stanford University Stanford University Kevin Arrigo Kevin Arrigo Department of Geophysics Department of Geophysics Stanford University Stanford University Computational Revision of Computational Revision of Ecological Process Models Ecological Process Models S. Dzeroski, J. Sanchez, K. Saito, J. Shrager, and L. Todorovski fo S. Dzeroski, J. Sanchez, K. Saito, J. Shrager, and L. Todorovski fo ions to this research, which is funded by the US National Science Fo ions to this research, which is funded by the US National Science Fo
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Nima Asgharbeygi, Pat Langley, Stephen Bay Center for the Study of Language and Information Stanford University Kevin Arrigo Department of Geophysics Stanford.
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Nima Asgharbeygi, Pat Langley, Stephen BayNima Asgharbeygi, Pat Langley, Stephen BayCenter for the Study of Language and InformationCenter for the Study of Language and Information
Stanford UniversityStanford University
Kevin ArrigoKevin ArrigoDepartment of Geophysics Department of Geophysics
Stanford UniversityStanford University
Computational Revision of Computational Revision of Ecological Process ModelsEcological Process Models
Thanks to S. Dzeroski, J. Sanchez, K. Saito, J. Shrager, and L. Todorovski for their Thanks to S. Dzeroski, J. Sanchez, K. Saito, J. Shrager, and L. Todorovski for their contributions to this research, which is funded by the US National Science Foundation.contributions to this research, which is funded by the US National Science Foundation.
Data Mining vs. Scientific DiscoveryData Mining vs. Scientific Discovery
induce predictive models from large (often business) data sets;induce predictive models from large (often business) data sets; represent models in notations invented by AI researchers.represent models in notations invented by AI researchers.
There exist two computational paradigms for discovering explicit There exist two computational paradigms for discovering explicit knowledge from data. knowledge from data.
The The data miningdata mining movement develops computational methods that: movement develops computational methods that:
This talk focuses on applications of the second framework to This talk focuses on applications of the second framework to environmental and ecosystem modeling. environmental and ecosystem modeling.
constructing models from (often small) scientific data sets;constructing models from (often small) scientific data sets; stated in formalisms invented by scientists themselves.stated in formalisms invented by scientists themselves.
Phytoplankton loss is a Phytoplankton loss is a processprocess that affects two variables; no model that affects two variables; no model should include one influence without the other.should include one influence without the other.
Grazing in the Ross Sea EcosystemGrazing in the Ross Sea Ecosystem
We can view an ecosystem model as a set of processes that provide We can view an ecosystem model as a set of processes that provide an alternative way to encode its assumptions. an alternative way to encode its assumptions.
Process Model of Ross Sea EcosystemProcess Model of Ross Sea Ecosystem
process exponential_growth process exponential_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1,equations: d[P,t] = [0, 1,] ] P P
process logistic_growthprocess logistic_growth variables: P {population}variables: P {population} equations: d[P,t] = [0, 1, equations: d[P,t] = [0, 1, ] ] P P (1 (1 P / [0, 1, P / [0, 1, ])])
process constant_inflowprocess constant_inflow variables: I {inorganic_nutrient}variables: I {inorganic_nutrient} equations: d[I,t] = [0, 1, equations: d[I,t] = [0, 1, ]]
process no_saturationprocess no_saturation variables: P {number}, nutrient_P {number}variables: P {number}, nutrient_P {number} equations: nutrient_P = Pequations: nutrient_P = P
process saturationprocess saturation variables: P {number}, nutrient_P {number}variables: P {number}, nutrient_P {number} equations: nutrient_P = P / (P + [0, 1, equations: nutrient_P = P / (P + [0, 1, ])])
generic processesgeneric processes
Generic Processes for Aquatic EcosystemsGeneric Processes for Aquatic Ecosystems
generic process exponential_lossgeneric process exponential_loss generic process remineralizationgeneric process remineralization variables: S{species}, D{detritus}variables: S{species}, D{detritus} variables: N{nutrient}, variables: N{nutrient}, D{detritus}D{detritus} parameters: parameters: [0, 1] [0, 1] parameters: parameters: [0, 1] [0, 1] equations:equations: d[S,t,1] = d[S,t,1] = 1 1 S S equations: equations: d[N, t,1] = d[N, t,1] = D D
d[D,t,1] = d[D,t,1] = S S d[D, t,1] = d[D, t,1] = 1 1 DD
generic process nutrient_uptakegeneric process nutrient_uptake variables: S{species}, N{nutrient}variables: S{species}, N{nutrient} parameters: parameters: [0, [0, ], ], [0, 1], [0, 1], [0, 1] [0, 1] conditions:conditions: N > N > equations:equations: d[S,t,1] = d[S,t,1] = S S
d[N,t,1] = d[N,t,1] = 1 1 S S
A Method for Process Model RevisionA Method for Process Model Revision
1. Find all ways to instantiate available generic processes with 1. Find all ways to instantiate available generic processes with specific variables, subject to type constraints;specific variables, subject to type constraints;
2. Generate candidate model structures by deleting the current 2. Generate candidate model structures by deleting the current processes and adding new ones, subject to complexity limits; processes and adding new ones, subject to complexity limits;
3. For each generic model, carry out search through parameter 3. For each generic model, carry out search through parameter space to find good coefficients [difficult];space to find good coefficients [difficult];
4. Return a list of revised models ordered by their overall scores.4. Return a list of revised models ordered by their overall scores.
We have implemented RPM, an algorithm that revises an initial We have implemented RPM, an algorithm that revises an initial process model in four main stages:process model in four main stages:
The evaluation metric can be squared error or description length The evaluation metric can be squared error or description length based on error and distance from the initial model.based on error and distance from the initial model.
Observations from the Ross SeaObservations from the Ross Sea
Revised Model of Ross Sea EcosystemRevised Model of Ross Sea Ecosystem
Initial Results on Ross Sea Training DataInitial Results on Ross Sea Training Data
The best revised model reproduces the observations quite well.The best revised model reproduces the observations quite well.
Initial Results on Ross Sea Test DataInitial Results on Ross Sea Test Data
But the model predicts nearly the same behavior for both years.But the model predicts nearly the same behavior for both years.
Revised Results on Ross Sea Test DataRevised Results on Ross Sea Test Data
Refitting initial values for zooplankton gives better generalization.Refitting initial values for zooplankton gives better generalization.
Results on Data from Protist StudyResults on Data from Protist Study
Results on Data from Rinkobing FjordResults on Data from Rinkobing Fjord
specify a quantitative process model of the target system;specify a quantitative process model of the target system;
display and edit the model’s structure and details graphically;display and edit the model’s structure and details graphically;
simulate the model’s behavior over time and situations;simulate the model’s behavior over time and situations;
compare the model’s predicted behavior to observations; compare the model’s predicted behavior to observations;
invoke a revision module in response to detected anomalies.invoke a revision module in response to detected anomalies.
Because few scientists want to be replaced, we are developing Because few scientists want to be replaced, we are developing PPROMETHEUSROMETHEUS, an interactive environment that lets users:, an interactive environment that lets users:
The environment offers computational assistance in forming and The environment offers computational assistance in forming and evaluating models but lets the user retain control. evaluating models but lets the user retain control.
Interfacing with ScientistsInterfacing with Scientists
Viewing and Editing a Process ModelViewing and Editing a Process Model
computational scientific discovery (e.g., Langley et al., 1983);computational scientific discovery (e.g., Langley et al., 1983);
theory revision in machine learning (e.g., Towell, 1991);theory revision in machine learning (e.g., Towell, 1991);
qualitative physics and simulation (e.g., Forbus, 1984);qualitative physics and simulation (e.g., Forbus, 1984);
languages for scientific simulation (e.g., languages for scientific simulation (e.g., STELLA, MATLABSTELLA, MATLAB););
interactive tools for data analysis (e.g., Schneiderman, 2001).interactive tools for data analysis (e.g., Schneiderman, 2001).
Intellectual InfluencesIntellectual Influences
Our approach to computational discovery incorporates ideas from Our approach to computational discovery incorporates ideas from many traditions:many traditions:
Our work combines ideas from machine learning, AI, programming Our work combines ideas from machine learning, AI, programming languages, and human-computer interaction.languages, and human-computer interaction.
Directions for Future ResearchDirections for Future Research
produce additional results on other ecosystem modeling tasksproduce additional results on other ecosystem modeling tasks
develop improved methods for fitting model parametersdevelop improved methods for fitting model parameters
implement heuristic methods for searching the structure spaceimplement heuristic methods for searching the structure space
utilize knowledge of subsystems to further constrain searchutilize knowledge of subsystems to further constrain search
augment the modeling environment to make it more usableaugment the modeling environment to make it more usable
Despite our progress to date, we need further work in order to:Despite our progress to date, we need further work in order to:
Process modeling has great potential to aid model development Process modeling has great potential to aid model development in environmental science.in environmental science.
Contributions of the ResearchContributions of the Research
a new formalism for representing scientific process models;a new formalism for representing scientific process models;
an encoding for background knowledge as generic processes; an encoding for background knowledge as generic processes;
an algorithm for revising process models with time-series data;an algorithm for revising process models with time-series data;
an interactive environment for model construction/utilization.an interactive environment for model construction/utilization.
In summary, our work on computational discovery has produced:In summary, our work on computational discovery has produced:
We have demonstrated this approach to model revision on both We have demonstrated this approach to model revision on both ecosystem modeling and an environmental domain. ecosystem modeling and an environmental domain.
The PThe PROMETHEUSROMETHEUS modeling/revision environment is available at: modeling/revision environment is available at:
The Challenge of Systems ScienceThe Challenge of Systems Science
focusing on synthesis rather than analysis in their operation;focusing on synthesis rather than analysis in their operation;
using computer modeling as one of their central methods;using computer modeling as one of their central methods;
developing system-level models with many variables / relations;developing system-level models with many variables / relations;
evaluating models on observational, not experimental, data. evaluating models on observational, not experimental, data.
Disciplines like Earth science differ from traditional disciplines by:Disciplines like Earth science differ from traditional disciplines by:
Constructing such models are complex tasks that would benefit Constructing such models are complex tasks that would benefit from computational aids, but existing methods are insufficient. from computational aids, but existing methods are insufficient.
Why Are Process Models Interesting?Why Are Process Models Interesting?
they incorporate they incorporate scientific formalismsscientific formalisms rather than AI notations; rather than AI notations;
that are easily that are easily communicable communicable to scientists and engineers;to scientists and engineers;
they move beyond descriptive generalization to they move beyond descriptive generalization to explanationexplanation;;
while retaining the while retaining the modularitymodularity needed to support induction. needed to support induction.
Process models are a crucial target for machine learning because: Process models are a crucial target for machine learning because:
These reasons point to process models as an ideal representation These reasons point to process models as an ideal representation for scientific and engineering knowledge.for scientific and engineering knowledge.
Process models are an important alternative to formalisms used Process models are an important alternative to formalisms used currently in machine learning. currently in machine learning.
Advantages of Quantitative Process ModelsAdvantages of Quantitative Process Models
they embed quantitative relations within qualitative structure;they embed quantitative relations within qualitative structure;
that refer to notations and mechanisms familiar to experts;that refer to notations and mechanisms familiar to experts;
they provide dynamical predictions of changes over time;they provide dynamical predictions of changes over time;
they offer causal and explanatory accounts of phenomena;they offer causal and explanatory accounts of phenomena;
while retaining the modularity needed to support induction.while retaining the modularity needed to support induction.
Process models offer scientists a promising framework because: Process models offer scientists a promising framework because:
Quantitative process models provide an important alternative to Quantitative process models provide an important alternative to formalisms used currently in ecosystem modeling. formalisms used currently in ecosystem modeling.
Inductive Process ModelingInductive Process Modeling
Our response is to design, construct, and evaluate computational Our response is to design, construct, and evaluate computational methods for methods for inductive process modelinginductive process modeling, which: , which:
represent scientific models as sets of quantitative processes;represent scientific models as sets of quantitative processes;
use these models to predict and explain observational data;use these models to predict and explain observational data;
search a space of process models to find good candidates;search a space of process models to find good candidates;
utilize background knowledge to constrain this search. utilize background knowledge to constrain this search.
This framework has great potential to aid environmental science, This framework has great potential to aid environmental science, but it raises new computational challenges. but it raises new computational challenges.
Challenges of Inductive Process ModelingChallenges of Inductive Process Modeling
process models characterize behavior of dynamical systems; process models characterize behavior of dynamical systems;
variables are continuous but can have discontinuous behavior; variables are continuous but can have discontinuous behavior;
observations are not independently and identically distributed;observations are not independently and identically distributed;
models may contain unobservable processes and variables;models may contain unobservable processes and variables;
multiple processes can interact to produce complex behavior. multiple processes can interact to produce complex behavior.
Process model induction differs from typical learning tasks in that:Process model induction differs from typical learning tasks in that:
Compensating factors include a focus on deterministic systems and Compensating factors include a focus on deterministic systems and the availability of background knowledge. the availability of background knowledge.
Generating Predictions and ExplanationsGenerating Predictions and Explanations
To utilize or evaluate a given process model, we must simulate its To utilize or evaluate a given process model, we must simulate its behavior over time: behavior over time:
specify initial values for input variables and time step size;specify initial values for input variables and time step size;
on each time step, determine which processes are active;on each time step, determine which processes are active;
solve active algebraic/differential equations with known values;solve active algebraic/differential equations with known values;
propagate values and recursively solve other active equations; propagate values and recursively solve other active equations;
when multiple processes influence the same variable, assume when multiple processes influence the same variable, assume their effects are additive. their effects are additive.
This performance method makes specific predictions that we can This performance method makes specific predictions that we can compare to observations. compare to observations.
Generic Processes as Background KnowledgeGeneric Processes as Background Knowledge
the variables involved in a process and their types;the variables involved in a process and their types;
the parameters appearing in a process and their ranges; the parameters appearing in a process and their ranges;
the forms of conditions on the process; andthe forms of conditions on the process; and
the forms of associated equations and their parameters.the forms of associated equations and their parameters.
Our framework casts background knowledge as Our framework casts background knowledge as generic processesgeneric processes that specify: that specify:
Generic processes are building blocks from which one can compose Generic processes are building blocks from which one can compose a specific process model. a specific process model.
Estimating Parameters in Process ModelsEstimating Parameters in Process Models
1. Selects random initial values that fall within ranges specified 1. Selects random initial values that fall within ranges specified in the generic processes;in the generic processes;
2. Improves these parameters using the Levenberg-Marquardt 2. Improves these parameters using the Levenberg-Marquardt method until it reaches a local optimum;method until it reaches a local optimum;
3. Generates new candidate values through random jumps along 3. Generates new candidate values through random jumps along dimensions of the parameter vector and continue search; dimensions of the parameter vector and continue search;
4. If no improvement occurs after N jumps, it restarts the search 4. If no improvement occurs after N jumps, it restarts the search from a new random initial point.from a new random initial point.
To estimate the parameters for each generic model structure, the To estimate the parameters for each generic model structure, the IPM algorithm:IPM algorithm:
This multi-level method gives reasonable fits to time-series data This multi-level method gives reasonable fits to time-series data from a number of domains, but it is computationally intensive. from a number of domains, but it is computationally intensive.
A Process Model for an Aquatic EcosystemA Process Model for an Aquatic Ecosystem
generic process nutrient_uptakegeneric process nutrient_uptake variables: S{species}, N{nutrient}variables: S{species}, N{nutrient} parameters: parameters: [0, [0, ], ], [0, 1], [0, 1], [0, 1] [0, 1] conditions:conditions: N > N > equations:equations: d[S,t,1] = d[S,t,1] = S S
d[N,t,1] = d[N,t,1] = 1 1 S S
Inductive Process ModelingInductive Process Modeling
process exponential_growth process exponential_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1,equations: d[P,t] = [0, 1,] ] P P
process logistic_growthprocess logistic_growth variables: P {population}variables: P {population} equations: d[P,t] = [0, 1, equations: d[P,t] = [0, 1, ] ] P P (1 (1 P / [0, 1, P / [0, 1, ])])
process constant_inflowprocess constant_inflow variables: I {inorganic_nutrient}variables: I {inorganic_nutrient} equations: d[I,t] = [0, 1, equations: d[I,t] = [0, 1, ]]
process no_saturationprocess no_saturation variables: P {number}, nutrient_P {number}variables: P {number}, nutrient_P {number} equations: nutrient_P = Pequations: nutrient_P = P
process saturationprocess saturation variables: P {number}, nutrient_P {number}variables: P {number}, nutrient_P {number} equations: nutrient_P = P / (P + [0, 1, equations: nutrient_P = P / (P + [0, 1, ])])
Generic Processes for Photosynthesis RegulationGeneric Processes for Photosynthesis Regulation
generic process translationgeneric process translation generic process transcriptiongeneric process transcription variables: P{protein}, M{mRNA}variables: P{protein}, M{mRNA} variables: M{mRNA}, R{rate} variables: M{mRNA}, R{rate} parameters: parameters: [0, 1] [0, 1] parameters: parameters: equations:equations: d[P,t,1] = d[P,t,1] = M M equations: equations: d[M,t,1] = Rd[M,t,1] = R
generic process regulate_onegeneric process regulate_one generic process regulate_twogeneric process regulate_two variables: R{rate}, S{signal} variables: R{rate}, S{signal} variables: R{rate}, S{signal} variables: R{rate}, S{signal} parameters: parameters: [ [1 , 1] 1 , 1] parameters: parameters: [ [1 , 1], 1 , 1], [0, 1] [0, 1] equations:equations: R = R = S S equations: equations: R = R = S S
d[S, t,1] = d[S, t,1] = 1 1 S S
generic process automatic_degradationgeneric process automatic_degradation generic process controlled_degradationgeneric process controlled_degradation variables: C{concentration}variables: C{concentration} variables: D{concentration}, variables: D{concentration}, E{concentration}E{concentration} conditions:conditions: C > 0C > 0 conditions: conditions:D > 0, E > 0D > 0, E > 0 parameters: parameters: [0, 1] [0, 1] parameters: parameters: [0, 1] [0, 1] equations:equations: d[C,t,1] = d[C,t,1] = 1 1 C C equations: equations: d[D,t,1] = d[D,t,1] = 1 1 E E
d[E,t,1] = d[E,t,1] = 1 1 E Egeneric process photosynthesisgeneric process photosynthesis variables: L{light}, P{protein}, R{redox}, S{ROS}variables: L{light}, P{protein}, R{redox}, S{ROS} parameters: parameters: [0, 1], [0, 1], [0, 1] [0, 1] equations:equations: d[R,t,1] = d[R,t,1] = L L P P
d[S,t,1] = d[S,t,1] = L L P P
A Process Model for Photosynthetic RegulationA Process Model for Photosynthetic Regulation