Table of Contents
[ ii ]
Sum-product and belief updates 47
The junction tree algorithm 51
Examples of probabilistic graphical models 62
The sprinkler example 62
The medical expert system 63
Models with more than two layers 64
Tree structure 66
Summary 68
Chapter 3: Learning Parameters 69
Introduction 71
Learning by inference 75
Maximum likelihood 79
How are empirical and model distribution related? 79
The ML algorithm and its implementation in R 82
Application 86
Learning with hidden variables – the
EM algorithm 88
Latent variables 89
Principles of the EM algorithm 90
Derivation of the EM algorithm 91
Applying EM to graphical models 93
Summary 94
Chapter 4: Bayesian Modeling – Basic Models 97
The Naive Bayes model 98
Representation 100
Learning the Naive Bayes model 101
Bayesian Naive Bayes 104
Beta-Binomial 106
The prior distribution 111
The posterior distribution with the conjugacy property 112
Which values should we choose for the Beta parameters? 113
The Gaussian mixture model 115
Denition 116
Summary 122
Chapter 5: Approximate Inference 125
Sampling from a distribution 126
Basic sampling algorithms 129
Standard distributions 129
Rejection sampling 133
An implementation in R 135
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