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LES NOUVEAUX OUTILS DE L'ENTREPRISE DE DEMAIN

de Philippe Mounier

LES NOUVEAUX OUTILS DE L'ENTREPRISE DE DEMAIN




 


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Probabilistic Graphical Models - Principles and Techniques

Titre :

Probabilistic Graphical Models - Principles and Techniques

Caractéristiques :


Auteur(s) :D Koller
Editeur :M.I.T. PRESS
Parution :11/2009
Langue :Anglais Anglais
Nbre de pages :1208
ISBN :9780262013192
Reliure :Livre relié
Prix :113.00 € ttc
Disponibilité :En stock. Livraison sous 24h

Couverture :


Probabilistic Graphical Models - Principles and Techniques

Résumé :

Most tasks require a person or an automated system to reason—to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality.

Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty.

The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

Table des matières :

Complete Table of Contents

Acknowledgments
xxiii
List of Figures xxv
List of Algorithms xxxi
List of Boxes xxxiii
1 Introduction
1
1.1 Motivation 1
1.2 Structured Probabilistic Models 2
1.3 Overview and Roadmap 6
1.4 Historical Notes 12
2 Foundations 15
2.1 Probability Theory 15
2.2 Graphs 34
2.3 Relevant Literature 39
2.4 Exercises 39
I Representation 43
3 The Bayesian Network Representation 45
3.1 Exploiting Independence Properties 45
3.2 Bayesian Networks 51
3.3 Independencies in Graphs 68
3.4 From Distributions to Graphs 78
3.5 Summary 92
3.6 Relevant Literature 93
3.7 Exercises 96
4 Undirected Graphical Models 103
4.1 The Misconception Example 103
4.2 Parameterization 106
4.3 Markov Network Independencies 114
4.4 Parameterization Revisited 122
4.5 Bayesian Networks and Markov Networks 134
4.6 Partially Directed Models 142
4.7 Summary and Discussion 151
4.8 Relevant Literature 152
4.9 Exercises 153
5 Local Probabilistic Models 157
5.1 Tabular CPDs 157
5.2 Deterministic CPDs 158
5.3 Context-Specific CPDs 162
5.4 Independence of Causal Influence 175
5.5 Continuous Variables 185
5.6 Conditional Bayesian Networks 191
5.7 Summary 193
5.8 Relevant Literature 194
5.9 Exercises 195
6 Template-Based Representations 199
6.1 Introduction 199
6.2 Temporal Models 200
6.3 Template Variables and Template Factors 212
6.4 Directed Probabilistic Models for Object-Relational Domains 216
6.5 Undirected Representation 228
6.6 Structural Uncertainty 232
6.7 Summary 240
6.8 Relevant Literature 242
6.9 Exercises 243
7 Gaussian Network Models 247
7.1 Multivariate Gaussians 247
7.2 Gaussian Bayesian Networks 251
7.3 Gaussian Markov Random Fields 254
7.4 Summary 257
7.5 Relevant Literature 258
7.6 Exercises 258
8 The Exponential Family 261
8.1 Introduction 261
8.2 Exponential Families 261
8.3 Factored Exponential Families 266
8.4 Entropy and Relative Entropy 269
8.5 Projections 273
8.6 Summary 282
8.7 Relevant Literature 283
8.8 Exercises 283
II Inference 285
9 Exact Inference: Variable Elimination 287
9.1 Analysis of Complexity 288
9.2 Variable Elimination: The Basic Ideas 292
9.3 Variable Elimination 296
9.4 Complexity and Graph Structure: Variable Elimination 306
9.5 Conditioning 315
9.6 Inference with Structured CPDs 325
9.7 Summary and Discussion 336
9.8 Relevant Literature 337
9.9 Exercises 338
10 Exact Inference: Clique Trees 345
10.1 Variable Elimination and Clique Trees 345
10.2 Message Passing: Sum Product 348
10.3 Message Passing: Belief Update 364
10.4 Constructing a Clique Tree 372
10.5 Summary 376
10.6 Relevant Literature 377
10.7 Exercises 378
11 Inference as Optimization 381
11.1 Introduction 381
11.2 Exact Inference as Optimization 386
11.3 Propagation-Based Approximation 391
11.4 Propagation with Approximate Messages 430
11.5 Structured Variational Approximations 448
11.6 Summary and Discussion 473
11.7 Relevant Literature 475
11.8 Exercises 477
12 Particle-Based Approximate Inference 487
12.1 Forward Sampling 488
12.2 Likelihood Weighting and Importance Sampling 492
12.3 Markov Chain Monte Carlo Methods 505
12.4 Collapsed Particles 526
12.5 Deterministic Search Methods 536
12.6 Summary 540
12.7 Relevant Literature 541
12.8 Exercises 544
13 MAP Inference 551
13.1 Overview 551
13.2 Variable Elimination for (Marginal) MAP 554
13.3 Max-Product in Clique Trees 562
13.4 Max-Product Belief Propagation in Loopy Cluster Graphs 567
13.5 MAP as a Linear Optimization Problem 577
13.6 Using Graph Cuts for MAP 588
13.7 Local Search Algorithms 595
13.8 Summary 597
13.9 Relevant Literature 598
13.10 Exercises 601
14 Inference in Hybrid Networks 605
14.1 Introduction 605
14.2 Variable Elimination in Gaussian Networks 608
14.3 Hybrid Networks 615
14.4 Nonlinear Dependencies 630
14.5 Particle-Based Approximation Methods 642
14.6 Summary and Discussion 646
14.7 Relevant Literature 647
14.8 Exercises 649
15 Inference in Temporal Models 651
15.1 Inference Tasks 652
15.2 Exact Inference 653
15.3 Approximate Inference 660
15.4 Hybrid DBNs 675
15.5 Summary 688
15.6 Relevant Literature 690
15.7 Exercises 692
III Learning 695
16 Learning Graphical Models: Overview 697
16.1 Motivation 697
16.2 Goals of Learning 698
16.3 Learning as Optimization 702
16.4 Learning Tasks 711
16.5 Relevant Literature 715
17 Parameter Estimation 717
17.1 Maximum Likelihood Estimation 717
17.2 MLE for Bayesian Networks 722
17.3 Bayesian Parameter Estimation 733
17.4 Bayesian Parameter Estimation in Bayesian Networks 741
17.5 Learning Models with Shared Parameters 754
17.6 Generalization Analysis 769
17.7 Summary 776
17.8 Relevant Literature 777
17.9 Exercises 778
18 Structure Learning in Bayesian Networks 783
18.1 Introduction 783
18.2 Constraint-Based Approaches 786
18.3 Structure Scores 790
18.4 Structure Search 807
18.5 Bayesian Model Averaging 824
18.6 Learning Models with Additional Structure 832
18.7 Summary and Discussion 838
18.8 Relevant Literature 840
18.9 Exercises 843
19 Partially Observed Data 849
19.1 Foundations 849
19.2 Parameter Estimation 862
19.3 Bayesian Learning with Incomplete Data 897
19.4 Structure Learning 908
19.5 Learning Models with Hidden Variables 925
19.6 Summary 933
19.7 Relevant Literature 934
19.8 Exercises 935
20 Learning Undirected Models 943
20.1 Overview 943
20.2 The Likelihood Function 944
20.3 Maximum (Conditional) Likelihood Parameter Estimation 949
20.4 Parameter Priors and Regularization 958
20.5 Learning with Approximate Inference 961
20.6 Alternative Objectives 969
20.7 Structure Learning 978
20.8 Summary 996
20.9 Relevant Literature 998
20.10 Exercises 1001
IV Actions and Decisions 1007
21 Causality 1009
21.1 Motivation and Overview 1009
21.2 Causal Models 1014
21.3 Structural Causal Identifiability 1017
21.4 Mechanisms and Response Variables 1026
21.5 Partial Identifiability in Functional Causal Models 1031
21.6 Counterfactual Queries 1034
21.7 Learning Causal Models 1039
21.8 Summary 1052
21.9 Relevant Literature 1053
21.10 Exercises 1054
22 Utilities and Decisions 1057
22.1 Foundations: Maximizing Expected Utility 1057
22.2 Utility Curves 1062
22.3 Utility Elicitation 1066
22.4 Utilities of Complex Outcomes 1069
22.5 Summary 1079
22.6 Relevant Literature 1080
22.7 Exercises 1082
23 Structured Decision Problems 1083
23.1 Decision Trees 1083
23.2 Influence Diagrams 1086
23.3 Backward Induction in Influence Diagrams 1093
23.4 Computing Expected Utilities 1098
23.5 Optimization in Influence Diagrams 1105
23.6 Ignoring Irrelevant Information 1117
23.7 Value of Information 1119
23.8 Summary 1124
23.9 Relevant Literature 1125
23.10 Exercises 1128
24 Epilogue 1131
A Background Material 1135
A.1 Information Theory 1135
A.2 Convergence Bounds 1141
A.3 Algorithms and Algorithmic Complexity 1144
A.4 Combinatorial Optimization and Search 1152
A.5 Continuous Optimization 1159
Bibliography 1171
Notation Index
1209
Subject Index

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