What is included with this book?
Preface | p. ix |
Graphical models and probabilistic reasoning | p. 1 |
Introduction | p. 1 |
Axioms of probability and basic notations | p. 4 |
The Bayes update of probability | p. 9 |
Inductive learning | p. 11 |
Bayes' rule | p. 12 |
Jeffrey's rule | p. 13 |
Pearl's method of virtual evidence | p. 13 |
Interpretations of probability and Bayesian networks | p. 14 |
Learning as inference about parameters | p. 15 |
Bayesian statistical inference | p. 17 |
Tossing a thumb-tack | p. 20 |
Multinomial sampling and the Dirichlet integral | p. 24 |
Notes | p. 28 |
Exercises: Probabilistic theories of causality, Bayes' rule, multinomial sampling and the Dirichlet density | p. 31 |
Conditional independence, graphs and d-separation | p. 37 |
Joint probabilities | p. 37 |
Conditional independence | p. 38 |
Directed acyclic graphs and d-separation | p. 41 |
Graphs | p. 41 |
Directed acyclic graphs and probability distributions | p. 45 |
The Bayes ball | p. 50 |
Illustrations | p. 51 |
Potentials | p. 53 |
Bayesian networks | p. 58 |
Object oriented Bayesian networks | p. 63 |
d-Separation and conditional independence | p. 66 |
Markov models and Bayesian networks | p. 67 |
I-maps and Markov equivalence | p. 69 |
The trek and a distribution without a faithful graph | p. 72 |
Notes | p. 73 |
Exercises: Conditional independence and d-separation | p. 75 |
Evidence, sufficiency and Monte Carlo methods | p. 81 |
Hard evidence | p. 82 |
Soft evidence and virtual evidence | p. 85 |
Jeffrey's rule | p. 86 |
Pearl's method of virtual evidence | p. 87 |
Queries in probabilistic inference | p. 88 |
The chest clinic problem | p. 89 |
Bucket elimination | p. 89 |
Bayesian sufficient statistics and prediction sufficiency | p. 92 |
Bayesian sufficient statistics | p. 92 |
Prediction sufficiency | p. 92 |
Prediction sufficiency for a Bayesian network | p. 95 |
Time variables | p. 98 |
A brief introduction to Markov chain Monte Carlo methods | p. 100 |
Simulating a Markov chain | p. 103 |
Irreducibility, aperiodicity and time reversibility | p. 104 |
The Metropolis-Hastings algorithm | p. 108 |
The one-dimensional discrete Metropolis algorithm | p. 111 |
Notes | p. 112 |
Exercises: Evidence, sufficiency and Monte Carlo methods | p. 113 |
Decomposable graphs and chain graphs | p. 123 |
Definitions and notations | p. 124 |
Decomposable graphs and triangulation of graphs | p. 127 |
Junction trees | p. 131 |
Markov equivalence | p. 133 |
Markov equivalence, the essential graph and chain graphs | p. 138 |
Notes | p. 144 |
Exercises: Decomposable graphs and chain graphs | p. 145 |
Learning the conditional probability potentials | p. 149 |
Initial illustration: maximum likelihood estimate for a fork connection | p. 149 |
The maximum likelihood estimator for multinomial sampling | p. 151 |
MLE for the parameters in a DAG: the general setting | p. 155 |
Updating, missing data, fractional updating | p. 160 |
Notes | p. 161 |
Exercises: Learning the conditional probability potentials | p. 162 |
Learning the graph structure | p. 167 |
Assigning a probability distribution to the graph structure | p. 168 |
Markov equivalence and consistency | p. 171 |
Establishing the DAG isomorphic property | p. 173 |
Reducing the size of the search | p. 176 |
The Chow-Liu tree | p. 177 |
The Chow-Liu tree: A predictive approach | p. 179 |
The K2 structural learning algorithm | p. 183 |
The MMHC algorithm | p. 184 |
Monte Carlo methods for locating the graph structure | p. 186 |
Women in mathematics | p. 189 |
Notes | p. 191 |
Exercises: Learning the graph structure | p. 192 |
Parameters and sensitivity | p. 197 |
Changing parameters in a network | p. 198 |
Measures of divergence between probability distributions | p. 201 |
The Chan-Darwiche distance measure | p. 202 |
Comparison with the Kullback-Leibler divergence and euclidean distance | p. 209 |
Global bounds for queries | p. 210 |
Applications to updating | p. 212 |
Parameter changes to satisfy query constraints | p. 216 |
Binary variables | p. 218 |
The sensitivity of queries to parameter changes | p. 220 |
Notes | p. 224 |
Exercises: Parameters and sensitivity | p. 225 |
Graphical models and exponential families | p. 229 |
Introduction to exponential families | p. 229 |
Standard examples of exponential families | p. 231 |
Graphical models and exponential families | p. 233 |
Noisy 'or' as an exponential family | p. 234 |
Properties of the log partition function | p. 237 |
Fenchel Legendre conjugate | p. 239 |
Kullback-Leibler divergence | p. 241 |
Mean field theory | p. 243 |
Conditional Gaussian distributions | p. 246 |
CG potentials | p. 249 |
Some results on marginalization | p. 249 |
CG regression | p. 250 |
Notes | p. 251 |
Exercises: Graphical models and exponential families | p. 252 |
Causality and intervention calculus | p. 255 |
Introduction | p. 255 |
Conditioning by observation and by intervention | p. 257 |
The intervention calculus for a Bayesian network | p. 258 |
Establishing the model via a controlled experiment | p. 262 |
Properties of intervention calculus | p. 262 |
Transformations of probability | p. 265 |
A note on the order of 'see' and 'do' conditioning | p. 267 |
The 'Sure Thing' principle | p. 268 |
Back door criterion, confounding and identifiability | p. 270 |
Notes | p. 273 |
Exercises: Causality and intervention calculus | p. 275 |
The junction tree and probability updating | p. 279 |
Probability updating using a junction tree | p. 279 |
Potentials and the distributive law | p. 280 |
Marginalization and the distributive law | p. 283 |
Elimination and domain graphs | p. 284 |
Factorization along an undirected graph | p. 288 |
Factorizing along a junction tree | p. 290 |
Flow of messages initial illustration | p. 292 |
Local computation on junction trees | p. 294 |
Schedules | p. 296 |
Local and global consistency | p. 302 |
Message passing for conditional Gaussian distributions | p. 305 |
Using a junction tree with virtual evidence and soft evidence | p. 311 |
Notes | p. 313 |
Exercises: The junction tree and probability updating | p. 314 |
Factor graphs and the sum product algorithm | p. 319 |
Factorization and local potentials | p. 319 |
Examples of factor graphs | p. 320 |
The sum product algorithm | p. 323 |
Detailed illustration of the algorithm | p. 329 |
Notes | p. 332 |
Exercise: Factor graphs and the sum product algorithm | p. 333 |
References | p. 335 |
Index | p. 343 |
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