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| Preface | |
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| Prerequisites on Probability Theory | |
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| Two Perspectives on Probability Theory | |
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| Fundamentals of Probability Theory | |
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| Conditional Probabilities | |
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| Probability Calculus | |
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| Conditional Independence | |
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| Probability Calculus for Variables | |
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| Calculations with Probability Tables: An Example | |
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| An Algebra of Potentials | |
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| Random Variables | |
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| Continuous Distributions | |
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| Exercises | |
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| Probabilistic Graphical Models | |
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| Causal and Bayesian Networks | |
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| Reasoning Under Uncertainty | |
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| Car Start Problem | |
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| A Causal Perspective on the Car Start Problem | |
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| Causal Networks and d-Separation | |
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| d-separation | |
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| Bayesian Networks | |
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| Definition of Bayesian Networks | |
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| The Chain Rule for Bayesian Networks | |
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| Inserting Evidence | |
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| Calculating Probabilities in Practice | |
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| Graphical Models - Formal Languages for Model Specification | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Building Models | |
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| Catching the Structure | |
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| Milk Test | |
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| Cold or Angina? | |
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| Insemination | |
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| A Simplified Poker Game | |
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| Naive Bayes Models | |
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| Causality | |
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| Determining the Conditional Probabilities | |
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| Milk Test | |
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| Stud Farm | |
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| Poker Game | |
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| Transmission of Symbol Strings | |
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| Cold or Angina? | |
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| Why Causal Networks? | |
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| Modeling Methods | |
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| Undirected Relations | |
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| Noisy-Or | |
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| Divorcing | |
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| Noisy Functional Dependence | |
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| Expert Disagreements | |
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| Object-Oriented Bayesian Networks | |
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| Dynamic Bayesian Networks | |
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| How to Deal with Continuous Variables | |
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| Interventions | |
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| Special Features | |
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| Joint Probability Tables | |
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| Most-Probable Explanation | |
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| Data Conflict | |
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| Sensitivity Analysis | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Belief Updating in Bayesian Networks | |
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| Introductory Examples | |
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| A Single Marginal | |
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| Different Evidence Scenarios | |
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| All Marginals | |
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| Graph-Theoretic Representation | |
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| Task and Notation | |
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| Domain Graphs | |
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| Triangulated Graphs and Join Trees | |
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| Join Trees | |
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| Propagation in Junction Trees | |
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| Lazy Propagation in Junction Trees | |
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| Exploiting the Information Scenario | |
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| Barren Nodes | |
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| d-Separation | |
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| Nontriangulated Domain Graphs | |
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| Triangulation of Graphs | |
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| Triangulation of Dynamic Bayesian Networks | |
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| Exact Propagation with Bounded Space | |
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| Recursive Conditioning | |
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| Stochastic Simulation in Bayesian Networks | |
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| Probabilistic Logic Sampling | |
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| Likelihood Weighting | |
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| Gibbs Sampling | |
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| Loopy Belief Propagation | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Analysis Tools for Bayesian Networks | |
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| IEJ Trees | |
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| Joint Probabilities and A-Saturated Junction Trees | |
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| A-Saturated Junction Trees | |
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| Configuration of Maximal Probability | |
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| Axioms for Propagation in Junction Trees | |
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| Data Conflict | |
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| Insemination | |
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| The Conflict Measure conf | |
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| Conflict or Rare Case | |
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| Tracing of Conflicts | |
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| Other Approaches to Conflict Detection | |
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| SE Analysis | |
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| Example and Definitions | |
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| h-Saturated Junction Trees and SE Analysis | |
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| Sensitivity to Parameters | |
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| One-Way Sensitivity Analysis | |
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| Two-Way Sensitivity Analysis | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Parameter Estimation | |
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| Complete Data | |
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| Maximum Likelihood Estimation | |
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| Bayesian Estimation | |
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| Incomplete Data | |
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| Approximate Parameter Estimation: The EM Algorithm | |
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| Why We Cannot Perform Exact Parameter Estimation | |
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| Adaptation | |
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| Fractional Updating | |
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| Fading | |
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| Specification of an Initial Sample Size | |
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| Example: Strings of Symbols | |
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| Adaptation to Structure | |
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| Fractional Updating as an Approximation | |
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| Tuning | |
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| Example | |
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| Determining grad dist(x, y) as a Function of t | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Learning the Structure of Bayesian Networks | |
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| Constraint-Based Learning Methods | |
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| From Skeleton to DAG | |
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| From Independence Tests to Skeleton | |
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| Example | |
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| Constraint-Based Learning on Data Sets | |
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| Ockham's Razor | |
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| Score-Based Learning | |
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| Score Functions | |
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| Search Procedures | |
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| Chow-Liu Trees | |
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| Bayesian Score Functions | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Bayesian Networks as Classifiers | |
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| Naive Bayes Classifiers | |
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| Evaluation of Classifiers | |
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| Extensions of Naive Bayes Classifiers | |
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| Classification Trees | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Decision Graphs | |
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| Graphical Languages for Specification of Decision Problems | |
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| One-Shot Decision Problems | |
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| Fold or Call? | |
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| Mildew | |
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| One Decision in General | |
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| Utilities | |
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| Instrumental Rationality | |
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| Decision Trees | |
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| A Couple of Examples | |
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| Coalesced Decision Trees | |
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| Solving Decision Trees | |
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| Influence Diagrams | |
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| Extended Poker Model | |
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| Definition of Influence Diagrams | |
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| Repetitive Decision Problems | |
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| Asymmetric Decision Problems | |
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| Different Sources of Asymmetry | |
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| Unconstrained Influence Diagrams | |
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| Sequential Influence Diagrams | |
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| Decision Problems with Unbounded Time Horizons | |
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| Markov Decision Processes | |
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| Partially Observable Markov Decision Processes | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Solution Methods for Decision Graphs | |
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| Solutions to Influence Diagrams | |
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| The Chain Rule for Influence Diagrams | |
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| Strategies and Expected Utilities | |
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| An Example | |
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| Variable Elimination | |
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| Strong Junction Trees | |
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| Required Past | |
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| Policy Networks | |
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| Node Removal and Arc Reversal | |
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| Node Removal | |
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| Arc Reversal | |
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| An Example | |
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| Solutions to Unconstrained Influence Diagrams | |
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| Minimizing the S-DAG | |
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| Determining Policies and Step Functions | |
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| Decision Problems Without a Temporal Ordering: Troubleshooting | |
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| Action Sequences | |
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| A Greedy Approach | |
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| Call Service | |
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| Questions | |
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| Solutions to Decision Problems with Unbounded Time Horizon | |
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| A Basic Solution | |
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| Value Iteration | |
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| Policy Iteration | |
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| Solving Partially Observable Markov Decision Processes | |
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| Limited Memory Influence Diagrams | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| Methods for Analyzing Decision Problems | |
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| Value of Information | |
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| Test for Infected Milk? | |
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| Myopic Hypothesis-Driven Data Request | |
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| Non-Utility-Based Value Functions | |
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| Finding the Relevant Past and Future of a Decision Problem | |
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| Identifying the Required Past | |
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| Sensitivity Analysis | |
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| Example | |
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| One-Way Sensitivity Analysis in General | |
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| Summary | |
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| Bibliographical Notes | |
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| Exercises | |
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| List of Notation | |
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| References | |
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| Index | |