Graphical Models Representations for Learning, Reasoning and Data Mining

, by Borgelt, Christian; Steinbrecher, Matthias; Kruse, Rudolf R.

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ISBN: 9780470722107 | 047072210X
Cover: Hardcover
Copyright: 9/15/2009

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Graphical models are of increasing importance in applied statistics, and in particular in data mining. Providing a self-contained introduction and overview to learning relational, probabilistic, and possibilistic networks from data, this second edition of Graphical Models is thoroughly updated to include the latest research in this burgeoning field, including a new chapter on visualization. The text provides graduate students, and researchers with all the necessary background material, including modelling under uncertainty, decomposition of distributions, graphical representation of distributions, and applications relating to graphical models and problems for further research.

Preface	p. ix
Introduction	p. 1
Data and Knowledge	p. 2
Knowledge Discovery and Data Mining	p. 5
The KDD Process	p. 6
Data Mining Tasks	p. 7
Data Mining Methods	p. 8
Graphical Models	p. 10
Outline of this Book	p. 12
Imprecision and Uncertainty	p. 15
Modeling Inferences	p. 15
Imprecision and Relational Algebra	p. 17
Uncertainty and Probability Theory	p. 19
Possibility Theory and the Context Model	p. 21
Experiments with Dice	p. 22
The Context Model	p. 27
The Insufficient Reason Principle	p. 30
Overlapping Contexts	p. 31
Mathematical Formalization	p. 35
Normalization and Consistency	p. 37
Possibility Measures	p. 39
Mass Assignment Theory	p. 43
Degrees of Possibility for Decision Making	p. 45
Conditional Degrees of Possibility	p. 47
Imprecision and Uncertainty	p. 48
Open Problems	p. 48
Decomposition	p. 53
Decomposition and Reasoning	p. 54
Relational Decomposition	p. 55
A Simple Example	p. 55
Reasoning in the Simple Example	p. 57
Decomposability of Relations	p. 61
Tuple-Based Formalization	p. 63
Possibility-Based Formalization	p. 66
Conditional Possibility and Independence	p. 70
Probabilistic Decomposition	p. 74
A Simple Example	p. 74
Reasoning in the Simple Example	p. 76
Factorization of Probability Distributions	p. 77
Conditional Probability and Independence	p. 78
Possibilistic Decomposition	p. 82
Transfer from Relational Decomposition	p. 83
A Simple Example	p. 83
Reasoning in the Simple Example	p. 84
Conditional Degrees of Possibility and Independence	p. 85
Possibility versus Probability	p. 87
Graphical Representation	p. 93
Conditional Independence Graphs	p. 94
Axioms of Conditional Independence	p. 94
Graph Terminology	p. 97
Separation in Graphs	p. 100
Dependence and Independence Maps	p. 102
Markov Properties of Graphs	p. 106
Markov Equivalence of Graphs	p. 111
Graphs and Decompositions	p. 114
Markov Networks and Bayesian Networks	p. 120
Evidence Propagation in Graphs	p. 121
Propagation in Undirected Trees	p. 122
Join Tree Propagation	p. 128
Other Evidence Propagation Methods	p. 136
Computing Projections	p. 139
Databases of Sample Cases	p. 140
Relational and Sum Projections	p. 141
Expectation Maximization	p. 143
Maximum Projections	p. 148
A Simple Example	p. 149
Computation via the Support	p. 151
Computation via the Closure	p. 152
Experimental Evaluation	p. 155
Limitations	p. 156
Naive Classifiers	p. 157
Naive Bayes Classifiers	p. 157
The Basic Formula	p. 157
Relation to Bayesian Networks	p. 160
A Simple Example	p. 161
A Naive Possibilistic Classifier	p. 162
Classifier Simplification	p. 164
Experimental Evaluation	p. 164
Learning Global Structure	p. 167
Principles of Learning Global Structure	p. 168
Learning Relational Networks	p. 168
Learning Probabilistic Networks	p. 177
Learning Possibilistic Networks	p. 183
Components of a Learning Algorithm	p. 192
Evaluation Measures	p. 193
General Considerations	p. 193
Notation and Presuppositions	p. 197
Relational Evaluation Measures	p. 199
Probabilistic Evaluation Measures	p. 201
Possibilistic Evaluation Measures	p. 228
Search Methods	p. 230
Exhaustive Graph Search	p. 230
Greedy Search	p. 232
Guided Random Graph Search	p. 239
Conditional Independence Search	p. 247
Experimental Evaluation	p. 259
Learning Probabilistic Networks	p. 259
Learning Possibilistic Networks	p. 261
Learning Local Structure	p. 265
Local Network Structure	p. 265
Learning Local Structure	p. 267
Experimental Evaluation	p. 271
Inductive Causation	p. 273
Correlation and Causation	p. 273
Causal and Probabilistic Structure	p. 274
Faithfulness and Latent Variables	p. 276
The Inductive Causation Algorithm	p. 278
Critique of the Underlying Assumptions	p. 279
Evaluation	p. 284
Visualization	p. 287
Potentials	p. 288
Association Rules	p. 289
Applications	p. 295
Diagnosis of Electrical Circuits	p. 295
Iterative Proportional Fitting	p. 296
Modeling Electrical Circuits	p. 297
Constructing a Graphical Model	p. 299
A Simple Diagnosis Example	p. 301
Application in Telecommunications	p. 304
Application at Volkswagen	p. 307
Application at DaimlerChrysler	p. 310
Proofs of Theorems	p. 317
Proof of Theorem 4.1.2	p. 317
Proof of Theorem 4.1.18	p. 321
Proof of Theorem 4.1.20	p. 322
Proof of Theorem 4.1.26	p. 327
Proof of Theorem 4.1.28	p. 332
Proof of Theorem 4.1.30	p. 335
Proof of Theorem 4.1.31	p. 337
Proof of Theorem 5.4.8	p. 338
Proof of Lemma 7.2.2	p. 340
Proof of Lemma 7.2.4	p. 342
Proof of Lemma 7.2.6	p. 344
Proof of Theorem 7.3.1	p. 345
Proof of Theorem 7.3.2	p. 346
Proof of Theorem 7.3.3	p. 347
Proof of Theorem 7.3.5	p. 350
Proof of Theorem 7.3.7	p. 351
Software Tools	p. 353
Bibliography	p. 359
Index	p. 383
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Graphical Models Representations for Learning, Reasoning and Data Mining

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Graphical Models Representations for Learning, Reasoning and Data Mining

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