What is included with this book?
Complete Table of Contents | |
Acknowledgments | p. xxiii |
List of Figures | p. xxv |
List of Algorithms | p. xxxi |
List of Boxes | p. xxxiii |
Introduction | p. 1 |
Motivation | p. 1 |
Structured Probabilistic Models | p. 2 |
Overview and Roadmap | p. 6 |
Historical Notes | p. 12 |
Foundations | p. 15 |
Probability Theory | p. 15 |
Graphs | p. 34 |
Relevant Literature | p. 39 |
Exercises | p. 39 |
Representation | |
The Bayesian Network Representation | p. 45 |
Exploiting Independence Properties | p. 45 |
Bayesian Networks | p. 51 |
Independencies in Graphs | p. 68 |
From Distributions to Graphs | p. 78 |
Summary | p. 92 |
Relevant Literature | p. 93 |
Exercises | p. 96 |
Undirected Graphical Models | p. 103 |
The Misconception Example | p. 103 |
Parameterization | p. 106 |
Markov Network Independencies | p. 114 |
Parameterization Revisited | p. 122 |
Bayesian Networks and Markov Networks | p. 134 |
Partially Directed Models | p. 142 |
Summary and Discussion | p. 151 |
Relevant Literature | p. 152 |
Exercises | p. 153 |
Local Probabilistic Models | p. 157 |
Tabular CPDs | p. 157 |
Deterministic CPDs | p. 158 |
Context-Specific CPDs | p. 162 |
Independence of Causal Influence | p. 175 |
Continuous Variables | p. 185 |
Conditional Bayesian Networks | p. 191 |
Summary | p. 193 |
Relevant Literature | p. 194 |
Exercises | p. 195 |
Template-Based Representations | p. 199 |
Introduction | p. 199 |
Temporal Models | p. 200 |
Template Variables and Template Factors | p. 212 |
Directed Probabilistic Models for Object-Relational Domains | p. 216 |
Undirected Representation | p. 228 |
Structural Uncertainty | p. 232 |
Summary | p. 240 |
Relevant Literature | p. 242 |
Exercises | p. 243 |
Gaussian Network Models | p. 247 |
Multivariate Gaussians | p. 247 |
Gaussian Bayesian Networks | p. 251 |
Gaussian Markov Random Fields | p. 254 |
Summary | p. 257 |
Relevant Literature | p. 258 |
Exercises | p. 258 |
The Exponential Family | p. 261 |
Introduction | p. 261 |
Exponential Families | p. 261 |
Factored Exponential Families | p. 266 |
Entropy and Relative Entropy | p. 269 |
Projections | p. 273 |
Summary | p. 282 |
Relevant Literature | p. 283 |
Exercises | p. 283 |
Inference | |
Exact Inference: Variable Elimination | p. 287 |
Analysis of Complexity | p. 288 |
Variable Elimination: The Basic Ideas | p. 292 |
Variable Elimination | p. 296 |
Complexity and Graph Structure: Variable Elimination | p. 306 |
Conditioning | p. 315 |
Inference with Structured CPDs | p. 325 |
Summary and Discussion | p. 336 |
Relevant Literature | p. 337 |
Exercises | p. 338 |
Exact Inference: Clique Trees | p. 345 |
Variable Elimination and Clique Trees | p. 345 |
Message Passing: Sum Product | p. 348 |
Message Passing: Belief Update | p. 364 |
Constructing a Clique Tree | p. 372 |
Summary | p. 376 |
Relevant Literature | p. 377 |
Exercises | p. 378 |
Inference as Optimization | p. 381 |
Introduction | p. 381 |
Exact Inference as Optimization | p. 386 |
Propagation-Based Approximation | p. 391 |
Propagation with Approximate Messages | p. 430 |
Structured Variational Approximations | p. 448 |
Summary and Discussion | p. 473 |
Relevant Literature | p. 475 |
Exercises | p. 477 |
Particle-Based Approximate Inference | p. 487 |
Forward Sampling | p. 488 |
Likelihood Weighting and Importance Sampling | p. 492 |
Markov Chain Monte Carlo Methods | p. 505 |
Collapsed Particles | p. 526 |
Deterministic Search Methods | p. 536 |
Summary | p. 540 |
Relevant Literature | p. 541 |
Exercises | p. 544 |
MAP Inference | p. 551 |
Overview | p. 551 |
Variable Elimination for (Marginal) MAP | p. 554 |
Max-Product in Clique Trees | p. 562 |
Max-Product Belief Propagation in Loopy Cluster Graphs | p. 567 |
MAP as a Linear Optimization Problem | p. 577 |
Using Graph Cuts for MAP | p. 588 |
Local Search Algorithms | p. 595 |
Summary | p. 597 |
Relevant Literature | p. 598 |
Exercises | p. 601 |
Inference in Hybrid Networks | p. 605 |
Introduction | p. 605 |
Variable Elimination in Gaussian Networks | p. 608 |
Hybrid Networks | p. 615 |
Nonlinear Dependencies | p. 630 |
Particle-Based Approximation Methods | p. 642 |
Summary and Discussion | p. 646 |
Relevant Literature | p. 647 |
Exercises | p. 649 |
Inference in Temporal Models | p. 651 |
Inference Tasks | p. 652 |
Exact Inference | p. 653 |
Approximate Inference | p. 660 |
Hybrid DBNs | p. 675 |
Summary | p. 688 |
Relevant Literature | p. 690 |
Exercises | p. 692 |
Learning | |
Learning Graphical Models: Overview | p. 697 |
Motivation | p. 697 |
Goals of Learning | p. 698 |
Learning as Optimization | p. 702 |
Learning Tasks | p. 711 |
Relevant Literature | p. 715 |
Parameter Estimation | p. 717 |
Maximum Likelihood Estimation | p. 717 |
MLE for Bayesian Networks | p. 722 |
Bayesian Parameter Estimation | p. 733 |
Bayesian Parameter Estimation in Bayesian Networks | p. 741 |
Learning Models with Shared Parameters | p. 754 |
Generalization Analysis | p. 769 |
Summary | p. 776 |
Relevant Literature | p. 777 |
Exercises | p. 778 |
Structure Learning in Bayesian Networks | p. 783 |
Introduction | p. 783 |
Constraint-Based Approaches | p. 786 |
Structure Scores | p. 790 |
Structure Search | p. 807 |
Bayesian Model Averaging | p. 824 |
Learning Models with Additional Structure | p. 832 |
Summary and Discussion | p. 838 |
Relevant Literature | p. 840 |
Exercises | p. 843 |
Partially Observed Data | p. 849 |
Foundations | p. 849 |
Parameter Estimation | p. 862 |
Bayesian Learning with Incomplete Data | p. 897 |
Structure Learning | p. 908 |
Learning Models with Hidden Variables | p. 925 |
Summary | p. 933 |
Relevant Literature | p. 934 |
Exercises | p. 935 |
Learning Undirected Models | p. 943 |
Overview | p. 943 |
The Likelihood Function | p. 944 |
Maximum (Conditional) Likelihood Parameter Estimation | p. 949 |
Parameter Priors and Regularization | p. 958 |
Learning with Approximate Inference | p. 961 |
Alternative Objectives | p. 969 |
Structure Learning | p. 978 |
Summary | p. 996 |
Relevant Literature | p. 998 |
Exercises | p. 1001 |
Actions and Decisions | |
Causality | p. 1009 |
Motivation and Overview | p. 1009 |
Causal Models | p. 1014 |
Structural Causal Identifiability | p. 1017 |
Mechanisms and Response Variables | p. 1026 |
Partial Identifiability in Functional Causal Models | p. 1031 |
Counterfactual Queries | p. 1034 |
Learning Causal Models | p. 1039 |
Summary | p. 1052 |
Relevant Literature | p. 1053 |
Exercises | p. 1054 |
Utilities and Decisions | p. 1057 |
Foundations: Maximizing Expected Utility | p. 1057 |
Utility Curves | p. 1062 |
Utility Elicitation | p. 1066 |
Utilities of Complex Outcomes | p. 1069 |
Summary | p. 1079 |
Relevant Literature | p. 1080 |
Exercises | p. 1082 |
Structured Decision Problems | p. 1083 |
Decision Trees | p. 1083 |
Influence Diagrams | p. 1086 |
Backward Induction in Influence Diagrams | p. 1093 |
Computing Expected Utilities | p. 1098 |
Optimization in Influence Diagrams | p. 1105 |
Ignoring Irrelevant Information | p. 1117 |
Value of Information | p. 1119 |
Summary | p. 1124 |
Relevant Literature | p. 1125 |
Exercises | p. 1128 |
Epilogue | p. 1131 |
Background Material | p. 1135 |
Information Theory | p. 1135 |
Convergence Bounds | p. 1141 |
Algorithms and Algorithmic Complexity | p. 1144 |
Combinatorial Optimization and Search | p. 1152 |
Continuous Optimization | p. 1159 |
Bibliography | p. 1171 |
Notation Index | p. 1209 |
Subject Index | p. 1213 |
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