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Learning Bayesian Networks; Richard E. Neapolitan; Paperback: 674 pages Publisher: Prentice Hall; illustrated edition edition (April 6, 2003) Language: English ISBN-10: 0130125342 ISBN-13: 978-0130125347 Product Dimensions: 9.3 x 6.9 x 1.2 inches
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Learning Bay esian Netw orks
Richard E. Neapolitan
Northeastern Illinois University
Chicago, Illinois
In memory of m y dad, a difficult but loving father, who raised me well.
ii
Con ten ts
Preface ix
IBasics 1
1 Introduction to Bayesian Networks 3
1.1 BasicsofProbabilityTheory .................... 5
1.1.1 ProbabilityFunctionsandSpaces.............. 6
1.1.2 ConditionalProbabilityandIndependence......... 9
1.1.3 Bayes’Theorem ....................... 12
1.1.4 Random Variables and Joint Probability Distributions . . 13
1.2 BayesianInference .......................... 20
1.2.1 Random Variables and Probabilities in Bayesian Applica-
tions.............................. 20
1.2.2 A Definition of Random Variables and Joint Probability
DistributionsforBayesianInference ............ 24
1.2.3 AClassicalExampleofBayesianInference......... 27
1.3 LargeInstances/BayesianNetworks................ 29
1.3.1 The DifficultiesInherentinLargeInstances ........ 29
1.3.2 TheMarkovCondition.................... 31
1.3.3 BayesianNetworks...................... 40
1.3.4 ALargeBayesianNetwork ................. 43
1.4 CreatingBayesianNetworksUsingCausalEdges ......... 43
1.4.1 Ascert aining Causal Influences Using Manipulation . . . . 44
1.4.2 CausationandtheMarkovCondition ........... 51
2 M or e DAG/Probability Relation ships 65
2.1 EntailedConditionalIndependencies ................ 66
2.1.1 Examples of Entailed Conditional Independencies . . . . . 66
2.1.2 d-Separation ......................... 70
2.1.3 Findingd-Separations .................... 76
2.2 MarkovEquivalence ......................... 84
2.3 EntailingDependencieswithaDAG ................ 92
2.3.1 Faithfulness.......................... 95
iii
iv CONTENTS
2.3.2 EmbeddedFaithfulness ................... 99
2.4 Minimality ..............................104
2.5 MarkovBlanketsandBoundaries..................108
2.6 MoreonCausalDAGs........................110
2.6.1 TheCausalMinimalityAssumption ............110
2.6.2 TheCausalFaithfulnessAssumption............111
2.6.3 TheCausalEmbeddedFaithfulnessAssumption .....112
II Inference 121
3 Inference: Discrete Variables 123
3.1 ExamplesofInference ........................124
3.2 Pearl’sMessage-PassingAlgorithm .................126
3.2.1 InferenceinTrees.......................127
3.2.2 InferenceinSingly-ConnectedNetworks ..........142
3.2.3 InferenceinMultiply-ConnectedNetworks.........153
3.2.4 ComplexityoftheAlgorithm ................155
3.3 TheNoisyOR-GateModel .....................156
3.3.1 TheModel ..........................156
3.3.2 DoingInferenceWiththeModel ..............160
3.3.3 FurtherModels........................161
3.4 OtherAlgorithmsthatEmploytheDAG..............161
3.5 TheSPIAlgorithm..........................162
3.5.1 TheOptimalFactoringProblem ..............163
3.5.2 ApplicationtoProbabilisticInference ...........168
3.6 ComplexityofInference .......................170
3.7 RelationshiptoHumanReasoning .................171
3.7.1 TheCausalNetworkModel .................171
3.7.2 StudiesTestingtheCausalNetworkModel ........173
4 More Inference Algo rith ms 181
4.1 ContinuousVariableInference....................181
4.1.1 TheNormalDistribution ..................182
4.1.2 AnExampleConcerningContinuousVariables ......183
4.1.3 AnAlgorithmforContinuousVariables ..........185
4.2 ApproximateInference........................205
4.2.1 ABriefReviewofSampling.................205
4.2.2 LogicSampling........................211
4.2.3 LikelihoodWeighting.....................217
4.3 AbductiveInference .........................221
4.3.1 AbductiveInferenceinBayesianNetworks.........221
4.3.2 A Best-First Search Algorithm for Ab ductive Inference . . 224
CONTENTS v
5Influence Diagrams 239
5.1 DecisionTrees.............................239
5.1.1 SimpleExamples.......................239
5.1.2 Probabilities,Time,andRiskAttitudes ..........242
5.1.3 SolvingDecisionTrees....................245
5.1.4 MoreExamples........................245
5.2 InfluenceDiagrams..........................259
5.2.1 Representing with InfluenceDiagrams ...........259
5.2.2 Solving InfluenceDiagrams .................266
5.3 DynamicNetworks..........................272
5.3.1 DynamicBayesianNetworks ................272
5.3.2 Dynamic InfluenceDiagrams ................279
III Lea rning 291
6 Parameter Learning: Binary Variables 293
6.1 LearningaSingleParameter.....................294
6.1.1 Probability Distributions of Relative Frequencies . . . . . 294
6.1.2 LearningaRelativeFrequency ...............303
6.2 MoreontheBetaDensityFunction.................310
6.2.1 Non-integral Values of a and b ...............311
6.2.2 Assessing the Values of a and b ...............313
6.2.3 WhytheBetaDensityFunction?..............315
6.3 ComputingaProbabilityInterval..................319
6.4 LearningParametersinaBayesianNetwork............323
6.4.1 UrnExamples ........................323
6.4.2 AugmentedBayesianNetworks ...............331
6.4.3 Learning Using an Augmented Bayesian Network . . . . . 336
6.4.4 A Problem with Updating; Using an Equivalent Sample
Size ..............................348
6.5 LearningwithMissingDataItems .................357
6.5.1 DataItemsMissingatRandom...............358
6.5.2 DataItemsMissingNotatRandom ............363
6.6 VariancesinComputedRelativeFrequencies............364
6.6.1 ASimpleVarianceDetermination .............364
6.6.2 TheVarianceandEquivalentSampleSize.........366
6.6.3 ComputingVariancesinLargerNetworks .........372
6.6.4 WhenDoVariancesBecomeLarge? ............373
7 More Parameter Learni ng 381
7.1 MultinomialVariables ........................381
7.1.1 LearningaSingleParameter ................381
7.1.2 MoreontheDirichletDensityFunction ..........388
7.1.3 ComputingProbabilityIntervalsandRegions.......389
7.1.4 LearningParametersinaBayesianNetwork........392
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- 深無2014-06-09文字版的英文书,品质很好。
sanse1977
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