Timo Koski, John Noble

Bayesian Networks

An Introduction

• Gebundenes Buch

Produktbeschreibung

Bayesian networks have found application in a number of fields, including risk analysis, consumer help desks, tissue pathology, pattern recognition, credit assessment, computer network diagnosis, and artificial intelligence. Bayesian Networks is a self-contained introduction to the theory and applications of Bayesian networks. It introduces Bayesian networks, the Dirichlet distribution, exponential families and their applications and discusses graphical models, a topic with applications in the engineering and computer sciences. All concepts are clearly defined, illustrated with examples. An essential reference for postgraduate students of statistics, computer engineering and mathematics, data mining, artificial intelligence, computing and biology.

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Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout.

Features include:

An introduction to Dirichlet Distribution, Exponential Families and their applications.
A detailed description of learning algorithms and Conditional Gaussian Distributions using Junction Tree methods.
A discussion of Pearl's intervention calculus, with an introduction to the notion of see and do conditioning.
All concepts are clearly defined and illustrated with examples and exercises. Solutions are provided online.

This book will prove a valuable resource for postgraduate students of statistics, computer engineering, mathematics, data mining, artificial intelligence, and biology.

Researchers and users of comparable modelling or statistical techniques such as neural networks will also find this book of interest.

Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 14574304000
• 1. Auflage
• Seitenzahl: 368
• Erscheinungstermin: 1. November 2009
• Englisch
• Abmessung: 252mm x 177mm x 29mm
• Gewicht: 766g
• ISBN-13: 9780470743041
• ISBN-10: 0470743042
• Artikelnr.: 26876291

Autorenporträt

Timo Koski, Professor of Mathematical Statistics, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden. John M. Noble, Department of Mathematics, University of Linköping, Sweden.

Inhaltsangabe

Preface. 1 Graphical models and probabilistic reasoning. 1.1 Introduction.
1.2 Axioms of probability and basic notations. 1.3 The Bayes update of
probability. 1.4 Inductive learning. 1.5 Interpretations of probability and
Bayesian networks. 1.6 Learning as inference about parameters. 1.7 Bayesian
statistical inference. 1.8 Tossing a thumb-tack. 1.9 Multinomial sampling
and the Dirichlet integral. Notes. Exercises: Probabilistic theories of
causality, Bayes' rule, multinomial sampling and the Dirichlet density. 2
Conditional independence, graphs and d-separation. 2.1 Joint probabilities.
2.2 Conditional independence. 2.3 Directed acyclic graphs and d-separation.
2.4 The Bayes ball. 2.5 Potentials. 2.6 Bayesian networks. 2.7 Object
oriented Bayesian networks. 2.8 d-Separation and conditional independence.
2.9 Markov models and Bayesian networks. 2.10 I-maps and Markov
equivalence. Notes. Exercises: Conditional independence and d-separation. 3
Evidence, sufficiency and Monte Carlo methods. 3.1 Hard evidence. 3.2 Soft
evidence and virtual evidence. 3.3 Queries in probabilistic inference. 3.4
Bucket elimination. 3.5 Bayesian sufficient statistics and prediction
sufficiency. 3.6 Time variables. 3.7 A brief introduction to Markov chain
Monte Carlo methods. 3.8 The one-dimensional discrete Metropolis algorithm.
Notes. Exercises: Evidence, sufficiency and Monte Carlo methods. 4
Decomposable graphs and chain graphs. 4.1 Definitions and notations. 4.2
Decomposable graphs and triangulation of graphs. 4.3 Junction trees. 4.4
Markov equivalence. 4.5 Markov equivalence, the essential graph and chain
graphs. Notes. Exercises: Decomposable graphs and chain graphs. 5 Learning
the conditional probability potentials. 5.1 Initial illustration: maximum
likelihood estimate for a fork connection. 5.2 The maximum likelihood
estimator for multinomial sampling. 5.3 MLE for the parameters in a DAG:
the general setting. 5.4 Updating, missing data, fractional updating.
Notes. Exercises: Learning the conditional probability potentials. 6
Learning the graph structure. 6.1 Assigning a probability distribution to
the graph structure. 6.2 Markov equivalence and consistency. 6.3 Reducing
the size of the search. 6.4 Monte Carlo methods for locating the graph
structure. 6.5 Women in mathematics. Notes. Exercises: Learning the graph
structure. 7 Parameters and sensitivity. 7.1 Changing parameters in a
network. 7.2 Measures of divergence between probability distributions. 7.3
The Chan-Darwiche distance measure. 7.4 Parameter changes to satisfy query
constraints. 7.5 The sensitivity of queries to parameter changes. Notes.
Exercises: Parameters and sensitivity. 8 Graphical models and exponential
families. 8.1 Introduction to exponential families. 8.2 Standard examples
of exponential families. 8.3 Graphical models and exponential families. 8.4
Noisy 'or' as an exponential family. 8.5 Properties of the log partition
function. 8.6 Fenchel Legendre conjugate. 8.7 Kullback-Leibler divergence.
8.8 Mean field theory. 8.9 Conditional Gaussian distributions. Notes.
Exercises: Graphical models and exponential families. 9 Causality and
intervention calculus. 9.1 Introduction. 9.2 Conditioning by observation
and by intervention. 9.3 The intervention calculus for a Bayesian network.
9.4 Properties of intervention calculus. 9.5 Transformations of
probability. 9.6 A note on the order of 'see' and 'do' conditioning. 9.7
The 'Sure Thing' principle. 9.8 Back door criterion, confounding and
identifiability. Notes. Exercises: Causality and intervention calculus. 10
The junction tree and probability updating. 10.1 Probability updating using
a junction tree. 10.2 Potentials and the distributive law. 10.3 Elimination
and domain graphs. 10.4 Factorization along an undirected graph. 10.5
Factorizing along a junction tree. 10.6 Local computation on junction
trees. 10.7 Schedules. 10.8 Local and global consistency. 10.9 Message
passing for conditional Gaussian distributions. 10.10 Using a junction tree
with virtual evidence and soft evidence. Notes. Exercises: The junction
tree and probability updating. 11 Factor graphs and the sum product
algorithm. 11.1 Factorization and local potentials. 11.2 The sum product
algorithm. 11.3 Detailed illustration of the algorithm. Notes. Exercise:
Factor graphs and the sum product algorithm. References. Index.