| Preface |
| Graphical models and probabilistic reasoning / 1： |
| Introduction / 1.1： |
| Axioms of probability and basic notations / 1.2： |
| The Bayes update of probability / 1.3： |
| Inductive learning / 1.4： |
| Bayes' rule / 1.4.1： |
| Jeffrey's rule / 1.4.2： |
| Pearl's method of virtual evidence / 1.4.3： |
| Interpretations of probability and Bayesian networks / 1.5： |
| Learning as inference about parameters / 1.6： |
| Bayesian statistical inference / 1.7： |
| Tossing a thumb-tack / 1.8： |
| Multinomial sampling and the Dirichlet integral / 1.9： |
| Notes |
| Exercises: Probabilistic theories of causality, Bayes' rule, multinomial sampling and the Dirichlet density |
| Conditional independence, graphs and d-separation / 2： |
| Joint probabilities / 2.1： |
| Conditional independence / 2.2： |
| Directed acyclic graphs and d-separation / 2.3： |
| Graphs / 2.3.1： |
| Directed acyclic graphs and probability distributions / 2.3.2： |
| The Bayes ball / 2.4： |
| Illustrations / 2.4.1： |
| Potentials / 2.5： |
| Bayesian networks / 2.6： |
| Object oriented Bayesian networks / 2.7： |
| d-Separation and conditional independence / 2.8： |
| Markov models and Bayesian networks / 2.9： |
| I-maps and Markov equivalence / 2.10： |
| The trek and a distribution without a faithful graph / 2.10.1： |
| Exercises: Conditional independence and d-separation |
| Evidence, sufficiency and Monte Carlo methods / 3： |
| Hard evidence / 3.1： |
| Soft evidence and virtual evidence / 3.2： |
| Queries in probabilistic inference / 3.2.1： |
| The chest clinic problem / 3.3.1： |
| Bucket elimination / 3.4： |
| Bayesian sufficient statistics and prediction sufficiency / 3.5： |
| Bayesian sufficient statistics / 3.5.1： |
| Prediction sufficiency / 3.5.2： |
| Prediction sufficiency for a Bayesian network / 3.5.3： |
| Time variables / 3.6： |
| A brief introduction to Markov chain Monte Carlo methods / 3.7： |
| Simulating a Markov chain / 3.7.1： |
| Irreducibility, aperiodicity and time reversibility / 3.7.2： |
| The Metropolis-Hastings algorithm / 3.7.3： |
| The one-dimensional discrete Metropolis algorithm / 3.7.4： |
| Exercises: Evidence, sufficiency and Monte Carlo methods |
| Decomposable graphs and chain graphs / 4： |
| Definitions and notations / 4.1： |
| Decomposable graphs and triangulation of graphs / 4.2： |
| Junction trees / 4.3： |
| Markov equivalence / 4.4： |
| Markov equivalence, the essential graph and chain graphs / 4.5： |
| Exercises: Decomposable graphs and chain graphs |
| Learning the conditional probability potentials / 5： |
| Initial illustration: maximum likelihood estimate for a fork connection / 5.1： |
| The maximum likelihood estimator for multinomial sampling / 5.2： |
| MLE for the parameters in a DAG: the general setting / 5.3： |
| Updating, missing data, fractional updating / 5.4： |
| Exercises: Learning the conditional probability potentials |
| Learning the graph structure / 6： |
| Assigning a probability distribution to the graph structure / 6.1： |
| Markov equivalence and consistency / 6.2： |
| Establishing the DAG isomorphic property / 6.2.1： |
| Reducing the size of the search / 6.3： |
| The Chow-Liu tree / 6.3.1： |
| The Chow-Liu tree: A predictive approach / 6.3.2： |
| The K2 structural learning algorithm / 6.3.3： |
| The MMHC algorithm / 6.3.4： |
| Monte Carlo methods for locating the graph structure / 6.4： |
| Women in mathematics / 6.5： |
| Exercises: Learning the graph structure |
| Parameters and sensitivity / 7： |
| Changing parameters in a network / 7.1： |
| Measures of divergence between probability distributions / 7.2： |
| The Chan-Darwiche distance measure / 7.3： |
| Comparison with the Kullback-Leibler divergence and euclidean distance / 7.3.1： |
| Global bounds for queries / 7.3.2： |
| Applications to updating / 7.3.3： |
| Parameter changes to satisfy query constraints / 7.4： |
| Binary variables / 7.4.1： |
| The sensitivity of queries to parameter changes / 7.5： |
| Exercises: Parameters and sensitivity |
| Graphical models and exponential families / 8： |
| Introduction to exponential families / 8.1： |
| Standard examples of exponential families / 8.2： |
| Noisy 'or' as an exponential family / 8.3： |
| Properties of the log partition function / 8.5： |
| Fenchel Legendre conjugate / 8.6： |
| Kullback-Leibler divergence / 8.7： |
| Mean field theory / 8.8： |
| Conditional Gaussian distributions / 8.9： |
| CG potentials / 8.9.1： |
| Some results on marginalization / 8.9.2： |
| CG regression / 8.9.3： |
| Exercises: Graphical models and exponential families |
| Causality and intervention calculus / 9： |
| Conditioning by observation and by intervention / 9.1： |
| The intervention calculus for a Bayesian network / 9.3： |
| Establishing the model via a controlled experiment / 9.3.1： |
| Properties of intervention calculus / 9.4： |
| Transformations of probability / 9.5： |
| A note on the order of 'see' and 'do' conditioning / 9.6： |
| The 'Sure Thing' principle / 9.7： |
| Back door criterion, confounding and identifiability / 9.8： |
| Exercises: Causality and intervention calculus |
| The junction tree and probability updating / 10： |
| Probability updating using a junction tree / 10.1： |
| Potentials and the distributive law / 10.2： |
| Marginalization and the distributive law / 10.2.1： |
| Elimination and domain graphs / 10.3： |
| Factorization along an undirected graph / 10.4： |
| Factorizing along a junction tree / 10.5： |
| Flow of messages initial illustration / 10.5.1： |
| Local computation on junction trees / 10.6： |
| Schedules / 10.7： |
| Local and global consistency / 10.8： |
| Message passing for conditional Gaussian distributions / 10.9： |
| Using a junction tree with virtual evidence and soft evidence / 10.10： |
| Exercises: The junction tree and probability updating |
| Factor graphs and the sum product algorithm / 11： |
| Factorization and local potentials / 11.1： |
| Examples of factor graphs / 11.1.1： |
| The sum product algorithm / 11.2： |
| Detailed illustration of the algorithm / 11.3： |
| Exercise: Factor graphs and the sum product algorithm |
| References |
| Index |
| Preface |
| Graphical models and probabilistic reasoning / 1： |
| Introduction / 1.1： |
ＥＢ
図書
