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英文书名：Mastering Probabilistic Graphical Models Using Python
好像还没有中文译本吧，姑且称为《概率图模型：Python 实现》吧。
目录：
Preface vii
Chapter 1: Bayesian Network Fundamentals 1
Probability theory 2
Random variable 2
Independence and conditional independence 3
Installing tools 5
IPython 5
pgmpy 5
Representing independencies using pgmpy 6
Representing joint probability distributions using pgmpy 7
Conditional probability distribution 8
Representing CPDs using pgmpy 9
Graph theory 11
Nodes and edges 11
Walk, paths, and trails 12
Bayesian models 13
Representation 14
Factorization of a distribution over a network 16
Implementing Bayesian networks using pgmpy 17
Bayesian model representation 18
Reasoning pattern in Bayesian networks 20
D-separation 22
Direct connection 22
Indirect connection 22
Relating graphs and distributions 24
IMAP 24
IMAP to factorization 25
CPD representations 26
Deterministic CPDs 26
Context-specific CPDs 28
Tree CPD 28
Rule CPD 30
Summary 30
Chapter 2: Markov Network Fundamentals 31
Introducing the Markov network 32
Parameterizing a Markov network – factor 33
Factor operations 35
Gibbs distributions and Markov networks 38
The factor graph 42
Independencies in Markov networks 44
Constructing graphs from distributions 46
Bayesian and Markov networks 47
Converting Bayesian models into Markov models 47
Converting Markov models into Bayesian models 51
Chordal graphs 53
Summary 55
Chapter 3: Inference – Asking Questions to Models 57
Inference 57
Complexity of inference 59
Variable elimination 60
Analysis of variable elimination 66
Finding elimination ordering 69
Using the chordal graph property of induced graphs 71
Minimum fill/size/weight/search 71
Belief propagation 72
Clique tree 72
Constructing a clique tree 73
Message passing 76
Clique tree calibration 80
Message passing with division 82
Factor division 83
Querying variables that are not in the same cluster 88
MAP using variable elimination 90
Factor maximization 91
MAP using belief propagation 95
Finding the most probable assignment 96
Predictions from the model using pgmpy 97
A comparison of variable elimination and belief propagation 100
Summary 101
Chapter 4: Approximate Inference 103
The optimization problem 104
The energy function 106
Exact inference as an optimization 107
The propagation-based approximation algorithm 110
Cluster graph belief propagation 112
Constructing cluster graphs 115
Pairwise Markov networks 115
Bethe cluster graph 116
Propagation with approximate messages 117
Message creation 120
Inference with approximate messages 123
Sum-product expectation propagation 123
Belief update propagation 132
Sampling-based approximate methods 138
Forward sampling 139
Conditional probability distribution 141
Likelihood weighting and importance sampling 141
Importance sampling 142
Importance sampling in Bayesian networks 145
Computing marginal probabilities 147
Ratio likelihood weighting 147
Normalized likelihood weighting 147
Markov chain Monte Carlo methods 148
Gibbs sampling 148
Markov chains 149
The multiple transitioning model 152
Using a Markov chain 152
Collapsed particles 154
Collapsed importance sampling 155
Summary 158
Chapter 5: Model Learning – Parameter Estimation in
Bayesian Networks 159
General ideas in learning 160
The goals of learning 160
Density estimation 160
Predicting the specific probability values 162
Knowledge discovery 163
Learning as an optimization 163
Empirical risk and overfitting 164
Discriminative versus generative training 165
Learning task 165
Model constraints 165
Data observability 166
Parameter learning 166
Maximum likelihood estimation 166
Maximum likelihood principle 169
The maximum likelihood estimate for Bayesian networks 171
Bayesian parameter estimation 175
Priors 177
Bayesian parameter estimation for Bayesian networks 179
Structure learning in Bayesian networks 183
Methods for the learning structure 184
Constraint-based structure learning 185
Structure score learning 187
The likelihood score 187
The Bayesian score 190
The Bayesian score for Bayesian networks 193
Summary 196
Chapter 6: Model Learning – Parameter Estimation in
Markov Networks 197
Maximum likelihood parameter estimation 197
Likelihood function 198
Log-linear model 200
Gradient ascent 202
Learning with approximate inference 207
Belief propagation and pseudo-moment matching 208
Structure learning 210
Constraint-based structure learning 210
Score-based structure learning 212
The likelihood score 213
Bayesian score 214
Summary 216
Chapter 7: Specialized Models 217
The Naive Bayes model 217
Why does it even work? 220
Types of Naive Bayes models 223
Multivariate Bernoulli Naive Bayes model 224
Multinomial Naive Bayes model 229
Choosing the right model 231
Dynamic Bayesian networks 231
Assumptions 231
Discrete timeline assumption 232
The Markov assumption 232
Model representation 233
The Hidden Markov model 235
Generating an observation sequence 238
Computing the probability of an observation 242
The forward-backward algorithm 243
Computing the state sequence 247
Applications 251
The acoustic model 252
The language model 253
Summary 254
Index 255
Mastering Probabilistic Graphical Models using Python.pdf
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