Probabilistic Graphical Models

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  • Format: Hardcover
  • Copyright: 2009-08-31
  • Publisher: Mit Pr
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Most tasks require a person or an automated system to reason-to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Modelsdiscusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs. Adaptive Computation and Machine Learning series

Table of Contents

Complete Table of Contents
Acknowledgmentsp. xxiii
List of Figuresp. xxv
List of Algorithmsp. xxxi
List of Boxesp. xxxiii
Introductionp. 1
Motivationp. 1
Structured Probabilistic Modelsp. 2
Overview and Roadmapp. 6
Historical Notesp. 12
Foundationsp. 15
Probability Theoryp. 15
Graphsp. 34
Relevant Literaturep. 39
Exercisesp. 39
The Bayesian Network Representationp. 45
Exploiting Independence Propertiesp. 45
Bayesian Networksp. 51
Independencies in Graphsp. 68
From Distributions to Graphsp. 78
Summaryp. 92
Relevant Literaturep. 93
Exercisesp. 96
Undirected Graphical Modelsp. 103
The Misconception Examplep. 103
Parameterizationp. 106
Markov Network Independenciesp. 114
Parameterization Revisitedp. 122
Bayesian Networks and Markov Networksp. 134
Partially Directed Modelsp. 142
Summary and Discussionp. 151
Relevant Literaturep. 152
Exercisesp. 153
Local Probabilistic Modelsp. 157
Tabular CPDsp. 157
Deterministic CPDsp. 158
Context-Specific CPDsp. 162
Independence of Causal Influencep. 175
Continuous Variablesp. 185
Conditional Bayesian Networksp. 191
Summaryp. 193
Relevant Literaturep. 194
Exercisesp. 195
Template-Based Representationsp. 199
Introductionp. 199
Temporal Modelsp. 200
Template Variables and Template Factorsp. 212
Directed Probabilistic Models for Object-Relational Domainsp. 216
Undirected Representationp. 228
Structural Uncertaintyp. 232
Summaryp. 240
Relevant Literaturep. 242
Exercisesp. 243
Gaussian Network Modelsp. 247
Multivariate Gaussiansp. 247
Gaussian Bayesian Networksp. 251
Gaussian Markov Random Fieldsp. 254
Summaryp. 257
Relevant Literaturep. 258
Exercisesp. 258
The Exponential Familyp. 261
Introductionp. 261
Exponential Familiesp. 261
Factored Exponential Familiesp. 266
Entropy and Relative Entropyp. 269
Projectionsp. 273
Summaryp. 282
Relevant Literaturep. 283
Exercisesp. 283
Exact Inference: Variable Eliminationp. 287
Analysis of Complexityp. 288
Variable Elimination: The Basic Ideasp. 292
Variable Eliminationp. 296
Complexity and Graph Structure: Variable Eliminationp. 306
Conditioningp. 315
Inference with Structured CPDsp. 325
Summary and Discussionp. 336
Relevant Literaturep. 337
Exercisesp. 338
Exact Inference: Clique Treesp. 345
Variable Elimination and Clique Treesp. 345
Message Passing: Sum Productp. 348
Message Passing: Belief Updatep. 364
Constructing a Clique Treep. 372
Summaryp. 376
Relevant Literaturep. 377
Exercisesp. 378
Inference as Optimizationp. 381
Introductionp. 381
Exact Inference as Optimizationp. 386
Propagation-Based Approximationp. 391
Propagation with Approximate Messagesp. 430
Structured Variational Approximationsp. 448
Summary and Discussionp. 473
Relevant Literaturep. 475
Exercisesp. 477
Particle-Based Approximate Inferencep. 487
Forward Samplingp. 488
Likelihood Weighting and Importance Samplingp. 492
Markov Chain Monte Carlo Methodsp. 505
Collapsed Particlesp. 526
Deterministic Search Methodsp. 536
Summaryp. 540
Relevant Literaturep. 541
Exercisesp. 544
MAP Inferencep. 551
Overviewp. 551
Variable Elimination for (Marginal) MAPp. 554
Max-Product in Clique Treesp. 562
Max-Product Belief Propagation in Loopy Cluster Graphsp. 567
MAP as a Linear Optimization Problemp. 577
Using Graph Cuts for MAPp. 588
Local Search Algorithmsp. 595
Summaryp. 597
Relevant Literaturep. 598
Exercisesp. 601
Inference in Hybrid Networksp. 605
Introductionp. 605
Variable Elimination in Gaussian Networksp. 608
Hybrid Networksp. 615
Nonlinear Dependenciesp. 630
Particle-Based Approximation Methodsp. 642
Summary and Discussionp. 646
Relevant Literaturep. 647
Exercisesp. 649
Inference in Temporal Modelsp. 651
Inference Tasksp. 652
Exact Inferencep. 653
Approximate Inferencep. 660
Hybrid DBNsp. 675
Summaryp. 688
Relevant Literaturep. 690
Exercisesp. 692
Learning Graphical Models: Overviewp. 697
Motivationp. 697
Goals of Learningp. 698
Learning as Optimizationp. 702
Learning Tasksp. 711
Relevant Literaturep. 715
Parameter Estimationp. 717
Maximum Likelihood Estimationp. 717
MLE for Bayesian Networksp. 722
Bayesian Parameter Estimationp. 733
Bayesian Parameter Estimation in Bayesian Networksp. 741
Learning Models with Shared Parametersp. 754
Generalization Analysisp. 769
Summaryp. 776
Relevant Literaturep. 777
Exercisesp. 778
Structure Learning in Bayesian Networksp. 783
Introductionp. 783
Constraint-Based Approachesp. 786
Structure Scoresp. 790
Structure Searchp. 807
Bayesian Model Averagingp. 824
Learning Models with Additional Structurep. 832
Summary and Discussionp. 838
Relevant Literaturep. 840
Exercisesp. 843
Partially Observed Datap. 849
Foundationsp. 849
Parameter Estimationp. 862
Bayesian Learning with Incomplete Datap. 897
Structure Learningp. 908
Learning Models with Hidden Variablesp. 925
Summaryp. 933
Relevant Literaturep. 934
Exercisesp. 935
Learning Undirected Modelsp. 943
Overviewp. 943
The Likelihood Functionp. 944
Maximum (Conditional) Likelihood Parameter Estimationp. 949
Parameter Priors and Regularizationp. 958
Learning with Approximate Inferencep. 961
Alternative Objectivesp. 969
Structure Learningp. 978
Summaryp. 996
Relevant Literaturep. 998
Exercisesp. 1001
Actions and Decisions
Causalityp. 1009
Motivation and Overviewp. 1009
Causal Modelsp. 1014
Structural Causal Identifiabilityp. 1017
Mechanisms and Response Variablesp. 1026
Partial Identifiability in Functional Causal Modelsp. 1031
Counterfactual Queriesp. 1034
Learning Causal Modelsp. 1039
Summaryp. 1052
Relevant Literaturep. 1053
Exercisesp. 1054
Utilities and Decisionsp. 1057
Foundations: Maximizing Expected Utilityp. 1057
Utility Curvesp. 1062
Utility Elicitationp. 1066
Utilities of Complex Outcomesp. 1069
Summaryp. 1079
Relevant Literaturep. 1080
Exercisesp. 1082
Structured Decision Problemsp. 1083
Decision Treesp. 1083
Influence Diagramsp. 1086
Backward Induction in Influence Diagramsp. 1093
Computing Expected Utilitiesp. 1098
Optimization in Influence Diagramsp. 1105
Ignoring Irrelevant Informationp. 1117
Value of Informationp. 1119
Summaryp. 1124
Relevant Literaturep. 1125
Exercisesp. 1128
Epiloguep. 1131
Background Materialp. 1135
Information Theoryp. 1135
Convergence Boundsp. 1141
Algorithms and Algorithmic Complexityp. 1144
Combinatorial Optimization and Searchp. 1152
Continuous Optimizationp. 1159
Bibliographyp. 1171
Notation Indexp. 1209
Subject Indexp. 1213
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