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| Preface | |
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| Graphical models and probabilistic reasoning | |
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| Introduction | |
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| Axioms of probability and basic notations | |
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| The Bayes update of probability | |
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| Inductive learning | |
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| Bayes' rule | |
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| Jeffrey's rule | |
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| Pearl's method of virtual evidence | |
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| Interpretations of probability and Bayesian networks | |
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| Learning as inference about parameters | |
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| Bayesian statistical inference | |
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| Tossing a thumb-tack | |
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| Multinomial sampling and the Dirichlet integral | |
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| Notes | |
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| Exercises: Probabilistic theories of causality, Bayes' rule, multinomial sampling and the Dirichlet density | |
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| Conditional independence, graphs and d-separation | |
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| Joint probabilities | |
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| Conditional independence | |
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| Directed acyclic graphs and d-separation | |
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| Graphs | |
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| Directed acyclic graphs and probability distributions | |
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| The Bayes ball | |
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| Illustrations | |
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| Potentials | |
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| Bayesian networks | |
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| Object oriented Bayesian networks | |
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| d-Separation and conditional independence | |
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| Markov models and Bayesian networks | |
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| I-maps and Markov equivalence | |
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| The trek and a distribution without a faithful graph | |
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| Notes | |
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| Exercises: Conditional independence and d-separation | |
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| Evidence, sufficiency and Monte Carlo methods | |
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| Hard evidence | |
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| Soft evidence and virtual evidence | |
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| Jeffrey's rule | |
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| Pearl's method of virtual evidence | |
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| Queries in probabilistic inference | |
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| The chest clinic problem | |
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| Bucket elimination | |
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| Bayesian sufficient statistics and prediction sufficiency | |
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| Bayesian sufficient statistics | |
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| Prediction sufficiency | |
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| Prediction sufficiency for a Bayesian network | |
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| Time variables | |
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| A brief introduction to Markov chain Monte Carlo methods | |
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| Simulating a Markov chain | |
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| Irreducibility, aperiodicity and time reversibility | |
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| The Metropolis-Hastings algorithm | |
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| The one-dimensional discrete Metropolis algorithm | |
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| Notes | |
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| Exercises: Evidence, sufficiency and Monte Carlo methods | |
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| Decomposable graphs and chain graphs | |
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| Definitions and notations | |
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| Decomposable graphs and triangulation of graphs | |
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| Junction trees | |
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| Markov equivalence | |
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| Markov equivalence, the essential graph and chain graphs | |
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| Notes | |
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| Exercises: Decomposable graphs and chain graphs | |
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| Learning the conditional probability potentials | |
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| Initial illustration: maximum likelihood estimate for a fork connection | |
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| The maximum likelihood estimator for multinomial sampling | |
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| MLE for the parameters in a DAG: the general setting | |
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| Updating, missing data, fractional updating | |
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| Notes | |
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| Exercises: Learning the conditional probability potentials | |
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| Learning the graph structure | |
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| Assigning a probability distribution to the graph structure | |
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| Markov equivalence and consistency | |
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| Establishing the DAG isomorphic property | |
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| Reducing the size of the search | |
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| The Chow-Liu tree | |
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| The Chow-Liu tree: A predictive approach | |
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| The K2 structural learning algorithm | |
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| The MMHC algorithm | |
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| Monte Carlo methods for locating the graph structure | |
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| Women in mathematics | |
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| Notes | |
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| Exercises: Learning the graph structure | |
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| Parameters and sensitivity | |
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| Changing parameters in a network | |
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| Measures of divergence between probability distributions | |
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| The Chan-Darwiche distance measure | |
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| Comparison with the Kullback-Leibler divergence and euclidean distance | |
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| Global bounds for queries | |
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| Applications to updating | |
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| Parameter changes to satisfy query constraints | |
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| Binary variables | |
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| The sensitivity of queries to parameter changes | |
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| Notes | |
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| Exercises: Parameters and sensitivity | |
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| Graphical models and exponential families | |
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| Introduction to exponential families | |
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| Standard examples of exponential families | |
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| Graphical models and exponential families | |
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| Noisy 'or' as an exponential family | |
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| Properties of the log partition function | |
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| Fenchel Legendre conjugate | |
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| Kullback-Leibler divergence | |
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| Mean field theory | |
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| Conditional Gaussian distributions | |
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| CG potentials | |
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| Some results on marginalization | |
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| CG regression | |
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| Notes | |
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| Exercises: Graphical models and exponential families | |
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| Causality and intervention calculus | |
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| Introduction | |
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| Conditioning by observation and by intervention | |
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| The intervention calculus for a Bayesian network | |
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| Establishing the model via a controlled experiment | |
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| Properties of intervention calculus | |
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| Transformations of probability | |
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| A note on the order of 'see' and 'do' conditioning | |
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| The 'Sure Thing' principle | |
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| Back door criterion, confounding and identifiability | |
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| Notes | |
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| Exercises: Causality and intervention calculus | |
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| The junction tree and probability updating | |
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| Probability updating using a junction tree | |
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| Potentials and the distributive law | |
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| Marginalization and the distributive law | |
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| Elimination and domain graphs | |
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| Factorization along an undirected graph | |
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| Factorizing along a junction tree | |
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| Flow of messages initial illustration | |
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| Local computation on junction trees | |
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| Schedules | |
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| Local and global consistency | |
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| Message passing for conditional Gaussian distributions | |
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| Using a junction tree with virtual evidence and soft evidence | |
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| Notes | |
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| Exercises: The junction tree and probability updating | |
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| Factor graphs and the sum product algorithm | |
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| Factorization and local potentials | |
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| Examples of factor graphs | |
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| The sum product algorithm | |
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| Detailed illustration of the algorithm | |
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| Notes | |
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| Exercise: Factor graphs and the sum product algorithm | |
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| References | |
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| Index | |