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Nov 1998
ISBN 0262600323
648 pp.
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Learning in Graphical Models
Michael I. Jordan

"The state of the art presented by the experts in the field."
-- Ross D. Shachter, Department of Engineering-Economic Systems and Operations Research, Stanford University

Graphical models, a marriage between probability theory and graph theory, provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity. In particular, they play an increasingly important role in the design and analysis of machine learning algorithms. Fundamental to the idea of a graphical model is the notion of modularity: a complex system is built by combining simpler parts. Probability theory serves as the glue whereby the parts are combined, ensuring that the system as a whole is consistent and providing ways to interface models to data. Graph theory provides both an intuitively appealing interface by which humans can model highly interacting sets of variables and a data structure that lends itself naturally to the design of efficient general-purpose algorithms.

This book presents an in-depth exploration of issues related to learning within the graphical model formalism. Four chapters are tutorial chapters -- Robert Cowell on Inference for Bayesian Networks, David MacKay on Monte Carlo Methods, Michael I. Jordan et al. on Variational Methods, and David Heckerman on Learning with Bayesian Networks. The remaining chapters cover a wide range of topics of current research interest.

Table of Contents
 Series Forward
 Preface
I Inference
1 Introduction to Inference for Bayesian Networks
by Robert Cowell
2 Advanced Inference in Bayesian Networks
by Robert Cowell
3 Inference in Bayesian Networks using Nested Junction Trees
by Uffe Kjærulff
4 Bucket Elimination: A Unifying Framework for Probabilistic Inference
by R. Dechter
5 An Introduction to Variational Methods for Graphical Models
by Michael I. Jordan, Zoubin Ghahramani, Tommi S. Jaakkola and Lawrence K. Saul
6 Improving the Mean Field Approximation via the Use of Mixture Distributions
by Tommi S. Jaakkola and Michael I. Jordan
7 Introduction to Monte Carlo Methods
by D. J. C. MacKay
8 Suppressing Random Walks in Markov Chain Monte Carlo using Ordered Overrelaxation
by Radford M. Neal
II Independence
9 Chain Graphs and Symmetric Associations
by Thomas S. Richardson
10 The Multiinformation Function as a Tool for Measuring Stochastic Dependence
by M. Studený and J. Vejnarová
III Foundations for Learning
11 A Tutorial on Learning with Bayesian Networks
by David Heckerman
12 A View of the EM Algorithm that Justifies Incremental, Sparse, and Other Variants
by Radford M. Neal and Geoffrey E. Hinton
IV Learning from Data
13 Latent Variable Models
by Christopher M. Bishop
14 Stochastic Algorithms for Exploratory Data Analysis: Data Clustering and Data Visualization
by Joachim M. Buhman
15 Learning Bayesian Networks with Local Structure
by Nir Friedman and Moises Goldszmidt
16 Asymptotic Model Selection for Directed Networks with Hidden Variables
by Dan Geige, David Heckermann and Christopher Meek
17 A Hierarchical Community of Experts
by Geoffrey E. Hingon, Brian Sallans and Zoubin Ghahramani
18 An Information-Theoretic Analysis of Hard and Soft Assignment Methods for Clustering
by Michael J. Kearns, Yishay Mansour and Andrew Y. Ng
19 Learning Hybrid Bayesian Networks from Data
by Stefano Monti and Gregory F. Cooper
20 A Mean Field Learning Algorithm for Unsupervised Neural Networks
by Lawrence Saul and Michael Jordan
21 Edge Exclusion Test for Graphical Gaussian Models
by Peter W. F. Smith and Joe Whittaker
22 Hepatitis B: A Case Study in MCMC
by D. J. Spiegelhalter, N. G. Best, W. R. Rilks and H. Inskip
23 Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond
by C. K. I. Williams
 Contributors
 Subject Index
 
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