Bayesian Artificial Intelligence, Second Edition

479 Pages·2010·3.31 MB·English

by  Kevin B. Korb

Bayesian
Artificial
Intelligence
SECOND EDITION
Chapman & Hall/CRC
Computer Science and Data Analysis Series
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Published Titles
Bayesian Artificial Intelligence, Second Edition Introduction to Machine Learning
Kevin B. Korb and Ann E. Nicholson and Bioinformatics
Sushmita Mitra, Sujay Datta,
Clustering for Data Mining:
Theodore Perkins, and George Michailidis
A Data Recovery Approach
Boris Mirkin Microarray Image Analysis:
Computational Statistics Handbook with An Algorithmic Approach
MATLAB®, Second Edition Karl Fraser, Zidong Wang, and Xiaohui Liu
Wendy L. Martinez and Angel R. Martinez
Pattern Recognition Algorithms for
Correspondence Analysis and Data Data Mining
Coding with Java and R Sankar K. Pal and Pabitra Mitra
Fionn Murtagh
R Graphics
Design and Modeling for Computer Paul Murrell
Experiments
R Programming for Bioinformatics
Kai-Tai Fang, Runze Li, and Agus Sudjianto
Robert Gentleman
Exploratory Data Analysis with MATLAB®
Semisupervised Learning for
Wendy L. Martinez and Angel R. Martinez
Computational Linguistics
Exploratory Multivariate Analysis by Steven Abney
Example Using R
Statistical Computing with R
François Husson, Sébastien Lê, and Maria L. Rizzo
Jérôme Pagès
Introduction to Data Technologies
Paul Murrell
Bayesian
Artificial
Intelligence
SECOND EDITION
Kevin B. Korb
Ann E. Nicholson
CRC Press
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Contents
ListofFigures xvii
ListofTables xxi
Preface xxiii
AbouttheAuthors xxvii
I PROBABILISTICREASONING 1
1 BayesianReasoning 3
1.1 Reasoningunderuncertainty . . . . . . . . . . . . . . . . . . . . 3
1.2 UncertaintyinAI . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Probabilitycalculus . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Conditionalprobabilitytheorems . . . . . . . . . . . . . 8
1.3.2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Interpretationsofprobability . . . . . . . . . . . . . . . . . . . . 10
1.5 Bayesianphilosophy . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.1 Bayes’theorem. . . . . . . . . . . . . . . . . . . . . . . 12
1.5.2 Bettingandodds . . . . . . . . . . . . . . . . . . . . . . 14
1.5.3 Expectedutility . . . . . . . . . . . . . . . . . . . . . . 15
1.5.4 Dutchbooks . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.5 Bayesianreasoningexamples . . . . . . . . . . . . . . . 17
1.5.5.1 Breastcancer . . . . . . . . . . . . . . . . . . 17
1.5.5.2 Peoplev.Collins . . . . . . . . . . . . . . . . 18
1.6 ThegoalofBayesianAI . . . . . . . . . . . . . . . . . . . . . . 21
1.7 AchievingBayesianAI . . . . . . . . . . . . . . . . . . . . . . . 22
1.8 AreBayesiannetworksBayesian? . . . . . . . . . . . . . . . . . 22
1.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.10 Bibliographicnotes . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.11 Technicalnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 IntroducingBayesianNetworks 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Bayesiannetworkbasics . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Nodesandvalues . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vii
viii
2.2.3 Conditionalprobabilities . . . . . . . . . . . . . . . . . . 32
2.2.4 TheMarkovproperty. . . . . . . . . . . . . . . . . . . . 33
2.3 ReasoningwithBayesiannetworks . . . . . . . . . . . . . . . . . 33
2.3.1 Typesofreasoning . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Typesofevidence . . . . . . . . . . . . . . . . . . . . . 35
2.3.3 Reasoningwithnumbers . . . . . . . . . . . . . . . . . . 36
2.4 UnderstandingBayesiannetworks . . . . . . . . . . . . . . . . . 37
2.4.1 Representingthejointprobabilitydistribution. . . . . . . 37
2.4.2 Pearl’snetworkconstructionalgorithm . . . . . . . . . . 37
2.4.3 Compactnessandnodeordering . . . . . . . . . . . . . . 38
2.4.4 Conditionalindependence . . . . . . . . . . . . . . . . . 39
2.4.4.1 Causalchains . . . . . . . . . . . . . . . . . . 39
2.4.4.2 Commoncauses . . . . . . . . . . . . . . . . . 40
2.4.4.3 Commoneffects . . . . . . . . . . . . . . . . . 40
2.4.5 d-separation . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5 Moreexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5.1 Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5.2 Metastaticcancer . . . . . . . . . . . . . . . . . . . . . . 44
2.5.3 Asia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.7 Bibliographicnotes . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 InferenceinBayesianNetworks 55
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Exactinferenceinchains . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1 Twonodenetwork . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 Threenodechain . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Exactinferenceinpolytrees . . . . . . . . . . . . . . . . . . . . . 58
3.3.1 KimandPearl’smessagepassingalgorithm . . . . . . . . 59
3.3.2 Messagepassingexample . . . . . . . . . . . . . . . . . 62
3.3.3 Algorithmfeatures . . . . . . . . . . . . . . . . . . . . . 64
3.4 Inferencewithuncertainevidence . . . . . . . . . . . . . . . . . 64
3.4.1 Usingavirtualnode . . . . . . . . . . . . . . . . . . . . 65
3.4.2 Virtualnodesinthemessagepassingalgorithm . . . . . . 67
3.4.3 Multiplevirtualevidence. . . . . . . . . . . . . . . . . . 67
3.5 Exactinferenceinmultiply-connectednetworks . . . . . . . . . . 69
3.5.1 Clusteringmethods. . . . . . . . . . . . . . . . . . . . . 69
3.5.2 Junctiontrees . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Approximateinferencewithstochasticsimulation . . . . . . . . . 74
3.6.1 Logicsampling . . . . . . . . . . . . . . . . . . . . . . . 75
3.6.2 Likelihoodweighting . . . . . . . . . . . . . . . . . . . 76
3.6.3 MarkovChainMonteCarlo(MCMC) . . . . . . . . . . . 78
3.6.4 Usingvirtualevidence . . . . . . . . . . . . . . . . . . . 78
3.6.5 Assessingapproximateinferencealgorithms . . . . . . . 78
ix
3.7 Othercomputations . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.7.1 Beliefrevision . . . . . . . . . . . . . . . . . . . . . . . 80
3.7.2 Probabilityofevidence. . . . . . . . . . . . . . . . . . . 80
3.8 Causalinference . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.8.1 Observationvs.intervention . . . . . . . . . . . . . . . . 81
3.8.2 Defininganintervention . . . . . . . . . . . . . . . . . . 83
3.8.3 Categoriesofintervention . . . . . . . . . . . . . . . . . 84
3.8.4 Modelingeffectiveness . . . . . . . . . . . . . . . . . . . 86
3.8.5 Representinginterventions . . . . . . . . . . . . . . . . . 87
3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.10 Bibliographicnotes . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4 DecisionNetworks 97
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2 Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3 Decisionnetworkbasics . . . . . . . . . . . . . . . . . . . . . . 99
4.3.1 Nodetypes . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3.2 Footballteamexample . . . . . . . . . . . . . . . . . . . 100
4.3.3 Evaluatingdecisionnetworks . . . . . . . . . . . . . . . 101
4.3.4 Informationlinks . . . . . . . . . . . . . . . . . . . . . . 102
4.3.5 Feverexample . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.6 Typesofactions . . . . . . . . . . . . . . . . . . . . . . 104
4.4 Sequentialdecisionmaking . . . . . . . . . . . . . . . . . . . . . 106
4.4.1 Test-actioncombination . . . . . . . . . . . . . . . . . . 106
4.4.2 Realestateinvestmentexample . . . . . . . . . . . . . . 107
4.4.3 Evaluationusingadecisiontreemodel . . . . . . . . . . 109
4.4.4 Valueofinformation . . . . . . . . . . . . . . . . . . . . 111
4.4.5 Directevaluationofdecisionnetworks . . . . . . . . . . 112
4.5 DynamicBayesiannetworks . . . . . . . . . . . . . . . . . . . . 112
4.5.1 Nodes,structureandCPTs . . . . . . . . . . . . . . . . . 113
4.5.2 Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.5.3 InferencealgorithmsforDBNs . . . . . . . . . . . . . . 117
4.6 Dynamicdecisionnetworks . . . . . . . . . . . . . . . . . . . . . 118
4.6.1 Mobilerobotexample . . . . . . . . . . . . . . . . . . . 119
4.7 Object-orientedBayesiannetworks . . . . . . . . . . . . . . . . . 120
4.7.1 OOBNbasics . . . . . . . . . . . . . . . . . . . . . . . . 120
4.7.2 OOBNinference . . . . . . . . . . . . . . . . . . . . . . 122
4.7.3 OOBNexamples . . . . . . . . . . . . . . . . . . . . . . 123
4.7.4 “is-A”relationship:Classinheritance . . . . . . . . . . . 125
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.9 Bibliographicnotes . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127