Graphical models: representations for learning, reasoning and data mining
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester
Wiley
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in computational statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017718870&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references |
| Umfang: | VIII, 393 S. graph. Darst. |
| ISBN: | 9780470722107 |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 620f 2010 A 2899(2) |
|---|---|
| DE-BY-TUM_katkey | 1724627 |
| DE-BY-TUM_location | 01 |
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| adam_text |
Titel: Graphical models
Autor: Borgelt, Christian
Jahr: 2009
Contents
Preface
IX
Introduction 1
1.1 Data and Knowledge. 2
1-2 Knowledge Discovery and Data Mining . 5
1.2.1 The KDD Process. 6
1.2.2 Data Mining Tasks. 7
1.2.3 Data Mining Methods. 8
1.3 Graphical Models. 10
1.4 Outline of this Book. 12
Imprecision and Uncertainty 15
2.1 Modeling Inferences . 15
2.2 Imprecision and Relational Algebra. 17
2.3 Uncertainty and Probability Theory. 19
2.4 Possibility Theory and the Context Model. 21
2.4.1 Experiments with Dice. 22
2.4.2 The Context Model . 27
2.4.3 The Insufficient Reason Principle. 30
2.4.4 Overlapping Contexts. 31
2.4.5 Mathematical Formalization . 35
2.4.6 Normalization and Consistency. 37
2.4.7 Possibility Measures. 39
2.4.8 Mass Assignment Theory. 43
2.4.9 Degrees of Possibility for Decision Making. 45
2.4.10 Conditional Degrees of Possibility . 47
2.4.11 Imprecision and Uncertainty . 48
2.4.12 Open Problems. 48
Decomposition 53
3.1 Decomposition and Reasoning. 54
3-2 Relational Decomposition. 55
vi CONTENTS
3.2.1 A Simple Example. 55
3.2.2 Reasoning in the Simple Example . 57
3.2.3 Decomposability of Relations. 61
3.2.4 Tuple-Based Formalization. 63
3.2.5 Possibility-Based Formalization. 66
3.2.6 Conditional Possibility and Independence. 70
3-3 Probabilistic Decomposition. 74
3.3.1 A Simple Example. 74
3.3.2 Reasoning in the Simple Example . 76
3.3.3 Factorization of Probability Distributions. 77
3.3.4 Conditional Probability and Independence. 78
3.4 Possibilistic Decomposition.82
3.4.1 Transfer from Relational Decomposition. 83
3.4.2 A Simple Example. 83
3.4.3 Reasoning in the Simple Example . 84
3.4.4 Conditional Degrees of Possibility and Independence . . 85
3.5 Possibility versus Probability. 87
4 Graphical Representation 93
4.1 Conditional Independence Graphs . 94
4.1.1 Axioms of Conditional Independence. 94
4.1.2 Graph Terminology . 97
4.1.3 Separation in Graphs . 100
4.1.4 Dependence and Independence Maps. 102
4.1.5 Markov Properties of Graphs. 106
4.1.6 Markov Equivalence of Graphs. Ill
4.1.7 Graphs and Decompositions. 114
4.1.8 Markov Networks and Bayesian Networks. 120
4.2 Evidence Propagation in Graphs. 121
4.2.1 Propagation in Undirected Trees. 122
4.2.2 Join Tree Propagation. 128
4.2.3 Other Evidence Propagation Methods. 136
5 Computing Projections 139
5.1 Databases of Sample Cases .140
5-2 Relational and Sum Projections.141
5.3 Expectation Maximization.143
5.4 Maximum Projections.148
5.4.1 A Simple Example.149
5.4.2 Computation via the Support.151
5.4.3 Computation via the Closure.152
5.4.4 Experimental Evaluation.155
5.4.5 Limitations.156
CONTENTS vii
6 Naive Classifiers 157
6.1 Naive Bayes Classifiers. 157
6.1.1 The Basic Formula. 157
6.1.2 Relation to Bayesian Networks. 160
6.1.3 A Simple Example. 161
6.2 A Naive Possibilistic Classifier . 162
6.3 Classifier Simplification. 164
6.4 Experimental Evaluation. 164
7 Learning Global Structure 167
7.1 Principles of Learning Global Structure .168
7.1.1 Learning Relational Networks.168
7.1.2 Learning Probabilistic Networks.177
7.1.3 Learning Possibilistic Networks.183
7.1.4 Components of a Learning Algorithm .192
7.2 Evaluation Measures.193
7.2.1 General Considerations .193
7.2.2 Notation and Presuppositions.197
7.2.3 Relational Evaluation Measures.199
7.2.4 Probabilistic Evaluation Measures.201
7.2.5 Possibilistic Evaluation Measures.228
7.3 Search Methods.230
7.3.1 Exhaustive Graph Search.230
7.3.2 Greedy Search.232
7.3.3 Guided Random Graph Search.239
7.3.4 Conditional Independence Search.247
7.4 Experimental Evaluation.259
7.4.1 Learning Probabilistic Networks.259
7.4.2 Learning Possibilistic Networks.261
8 Learning Local Structure 265
8.1 Local Network Structure.265
8.2 Learning Local Structure .^"'
8.3 Experimental Evaluation.^'*
9 Inductive Causation 273
9.1 Correlation and Causation.
9.2 Causal and Probabilistic Structure.274
9.3 Faithfulness and Latent Variables .276
9.4 The Inductive Causation Algorithm .278
9.5 Critique of the Underlying Assumptions.279
9.6 Evaluation .284
viii CONTENTS
10 Visualization 287
10.1 Potentials.288
10.2 Association Rules.289
11 Applications 295
11.1 Diagnosis of Electrical Circuits.295
11.1.1 Iterative Proportional Fitting.296
11.1.2 Modeling Electrical Circuits.297
11.1.3 Constructing a Graphical Model.299
11.1.4 A Simple Diagnosis Example.301
11.2 Application in Telecommunications.304
11.3 Application at Volkswagen .307
11.4 Application at DaimlerChrysler.310
A Proofs of Theorems 317
A.I Proof of Theorem 4.1.2.317
A.2 Proof of Theorem 4.1.18.321
A.3 Proof of Theorem 4.1.20.322
A.4 Proof of Theorem 4.1.26.327
A.5 Proof of Theorem 4.1.28.332
A.6 Proof of Theorem 4.1.30.335
A.7 Proof of Theorem 4.1.31.337
A.8 Proof of Theorem 5.4.8.338
A.9 Proof of Lemma 7.2.2 .340
A.10 Proof of Lemma 7.2.4 .342
A.ll Proof of Lemma 7.2.6 .344
A.12 Proof of Theorem 7.3.1.345
A.13 Proof of Theorem 7.3.2.346
A.14 Proof of Theorem 7.3.3.347
A.15 Proof of Theorem 7.3.5.350
A.16 Proof of Theorem 7.3.7.351
B Software Tools 353
Bibliography 359
Index 383 |
| any_adam_object | 1 |
| author | Borgelt, Christian 1967- Steinbrecher, Matthias Kruse, Rudolf 1952- |
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| author_role | aut aut aut |
| author_sort | Borgelt, Christian 1967- |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 006.321 519.5 |
| dewey-hundreds | 000 - Computer science, information, general works 500 - Natural sciences and mathematics |
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| dewey-tens | 000 - Computer science, information, general works 510 - Mathematics |
| discipline | Informatik Psychologie Mathematik Wirtschaftswissenschaften Geographie |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2025-02-10T13:13:59Z |
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| language | English |
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| spellingShingle | Borgelt, Christian 1967- Steinbrecher, Matthias Kruse, Rudolf 1952- Graphical models representations for learning, reasoning and data mining Graphical modeling (Statistics) Data mining Mathematical statistics -- Graphic methods Methode (DE-588)4038971-6 gnd Data Mining (DE-588)4428654-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4038971-6 (DE-588)4428654-5 (DE-588)4123037-1 |
| title | Graphical models representations for learning, reasoning and data mining |
| title_auth | Graphical models representations for learning, reasoning and data mining |
| title_exact_search | Graphical models representations for learning, reasoning and data mining |
| title_full | Graphical models representations for learning, reasoning and data mining Christian Borgelt, Matthias Steinbrecher & Rudolf Kruse |
| title_fullStr | Graphical models representations for learning, reasoning and data mining Christian Borgelt, Matthias Steinbrecher & Rudolf Kruse |
| title_full_unstemmed | Graphical models representations for learning, reasoning and data mining Christian Borgelt, Matthias Steinbrecher & Rudolf Kruse |
| title_short | Graphical models |
| title_sort | graphical models representations for learning reasoning and data mining |
| title_sub | representations for learning, reasoning and data mining |
| topic | Graphical modeling (Statistics) Data mining Mathematical statistics -- Graphic methods Methode (DE-588)4038971-6 gnd Data Mining (DE-588)4428654-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Graphical modeling (Statistics) Data mining Mathematical statistics -- Graphic methods Methode Data Mining Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017718870&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Teilbibliothek Mathematik & Informatik
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0102 MAT 620f 2010 A 2899(2) Lageplan |
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