Graphical Models -- Contents -- Preface -- 1 Introduction -- 1.1 Data and Knowledge -- 1.2 Knowledge Discovery and Data Mining -- 1.2.1 The KDD Process -- 1.2.2 Data Mining Tasks -- 1.2.3 Data Mining Methods -- 1.3 Graphical Models -- 1.4 Outline of this Book -- 2 Imprecision and Uncertainty -- 2.1 Modeling Inferences -- 2.2 Imprecision and Relational Algebra -- 2.3 Uncertainty and Probability Theory -- 2.4 Possibility Theory and the Context Model -- 2.4.1 Experiments with Dice -- 2.4.2 The Context Model -- 2.4.3 The Insufficient Reason Principle -- 2.4.4 Overlapping Contexts -- 2.4.5 Mathematical Formalization -- 2.4.6 Normalization and Consistency -- 2.4.7 Possibility Measures -- 2.4.8 Mass Assignment Theory -- 2.4.9 Degrees of Possibility for Decision Making -- 2.4.10 Conditional Degrees of Possibility -- 2.4.11 Imprecision and Uncertainty -- 2.4.12 Open Problems -- 3 Decomposition -- 3.1 Decomposition and Reasoning -- 3.2 Relational Decomposition -- 3.2.1 A Simple Example -- 3.2.2 Reasoning in the Simple Example -- 3.2.3 Decomposability of Relations -- 3.2.4 Tuple-Based Formalization -- 3.2.5 Possibility-Based Formalization -- 3.2.6 Conditional Possibility and Independence -- 3.3 Probabilistic Decomposition -- 3.3.1 A Simple Example -- 3.3.2 Reasoning in the Simple Example -- 3.3.3 Factorization of Probability Distributions -- 3.3.4 Conditional Probability and Independence -- 3.4 Possibilistic Decomposition -- 3.4.1 Transfer from Relational Decomposition -- 3.4.2 A Simple Example -- 3.4.3 Reasoning in the Simple Example -- 3.4.4 Conditional Degrees of Possibility and Independence -- 3.5 Possibility versus Probability -- 4 Graphical Representation -- 4.1 Conditional Independence Graphs -- 4.1.1 Axioms of Conditional Independence -- 4.1.2 Graph Terminology -- 4.1.3 Separation in Graphs -- 4.1.4 Dependence and Independence Maps.

4.1.5 Markov Properties of Graphs -- 4.1.6 Markov Equivalence of Graphs -- 4.1.7 Graphs and Decompositions -- 4.1.8 Markov Networks and Bayesian Networks -- 4.2 Evidence Propagation in Graphs -- 4.2.1 Propagation in Undirected Trees -- 4.2.2 Join Tree Propagation -- 4.2.3 Other Evidence Propagation Methods -- 5 Computing Projections -- 5.1 Databases of Sample Cases -- 5.2 Relational and Sum Projections -- 5.3 Expectation Maximization -- 5.4 Maximum Projections -- 5.4.1 A Simple Example -- 5.4.2 Computation via the Support -- 5.4.3 Computation via the Closure -- 5.4.4 Experimental Evaluation -- 5.4.5 Limitations -- 6 Naive Classifiers -- 6.1 Naive Bayes Classifiers -- 6.1.1 The Basic Formula -- 6.1.2 Relation to Bayesian Networks -- 6.1.3 A Simple Example -- 6.2 A Naive Possibilistic Classifier -- 6.3 Classifier Simplification -- 6.4 Experimental Evaluation -- 7 Learning Global Structure -- 7.1 Principles of Learning Global Structure -- 7.1.1 Learning Relational Networks -- 7.1.2 Learning Probabilistic Networks -- 7.1.3 Learning Possibilistic Networks -- 7.1.4 Components of a Learning Algorithm -- 7.2 Evaluation Measures -- 7.2.1 General Considerations -- 7.2.2 Notation and Presuppositions -- 7.2.3 Relational Evaluation Measures -- 7.2.4 Probabilistic Evaluation Measures -- 7.2.5 Possibilistic Evaluation Measures -- 7.3 Search Methods -- 7.3.1 Exhaustive Graph Search -- 7.3.2 Greedy Search -- 7.3.3 Guided Random Graph Search -- 7.3.4 Conditional Independence Search -- 7.4 Experimental Evaluation -- 7.4.1 Learning Probabilistic Networks -- 7.4.2 Learning Possibilistic Networks -- 8 Learning Local Structure -- 8.1 Local Network Structure -- 8.2 Learning Local Structure -- 8.3 Experimental Evaluation -- 9 Inductive Causation -- 9.1 Correlation and Causation -- 9.2 Causal and Probabilistic Structure -- 9.3 Faithfulness and Latent Variables.

9.4 The Inductive Causation Algorithm -- 9.5 Critique of the Underlying Assumptions -- 9.6 Evaluation -- 10 Visualization -- 10.1 Potentials -- 10.2 Association Rules -- 11 Applications -- 11.1 Diagnosis of Electrical Circuits -- 11.1.1 Iterative Proportional Fitting -- 11.1.2 Modeling Electrical Circuits -- 11.1.3 Constructing a Graphical Model -- 11.1.4 A Simple Diagnosis Example -- 11.2 Application in Telecommunications -- 11.3 Application at Volkswagen -- 11.4 Application at DaimlerChrysler -- A Proofs of Theorems -- A.1 Proof of Theorem 4.1.2 -- A.2 Proof of Theorem 4.1.18 -- A.3 Proof of Theorem 4.1.20 -- A.4 Proof of Theorem 4.1.26 -- A.5 Proof of Theorem 4.1.28 -- A.6 Proof of Theorem 4.1.30 -- A.7 Proof of Theorem 4.1.31 -- A.8 Proof of Theorem 5.4.8 -- A.9 Proof of Lemma 7.2.2 -- A.10 Proof of Lemma 7.2.4 -- A.11 Proof of Lemma 7.2.6 -- A.12 Proof of Theorem 7.3.1 -- A.13 Proof of Theorem 7.3.2 -- A.14 Proof of Theorem 7.3.3 -- A.15 Proof of Theorem 7.3.5 -- A.16 Proof of Theorem 7.3.7 -- B Software Tools -- Bibliography -- Index.