Graphical Models : Foundations of Neural Computation

by Michael I. Jordan and Terrence J. Sejnowski (Eds.)

• ISBN13: 9780262600422
• ISBN10: 0262600420
• Edition: 1st
• Format: Paperback
• Copyright: 2001-09-01
• Publisher: MIT PRESS

Summary

Graphical models use graphs to represent and manipulate joint probability distributions. They have their roots in artificial intelligence, statistics, and neural networks. The clean mathematical formalism of the graphical models framework makes it possible to understand a wide variety of network-based approaches to computation, and in particular to understand many neural network algorithms and architectures as instances of a broader probabilistic methodology. It also makes it possible to identify novel features of neural network algorithms and architectures and to extend them to more general graphical models. This book exemplifies the interplay between the general formal framework of graphical models and the exploration of new algorithms and architectures. The selections range from foundational papers of historical importance to results at the cutting edge of research. Contributors H. Attias, C. M. Bishop, B. J. Frey, Z. Ghahramani, D. Heckerman, G. E. Hinton, R. Hofmann, R. A. Jacobs, Michael I. Jordan, H. J. Kappen, A. Krogh, R. Neal, S. K. Riis, F. B. Rodríguez, L. K. Saul, Terrence J. Sejnowski, P. Smyth, M. E. Tipping, V. Tresp, Y. Weiss.

Table of Contents

Series Foreword	vii
Sources	ix
Introduction	xi
Probabilistic Independence Networks for Hidden Markov Probability Models	1	(44)
Padhraic Smyth
David Heckerman
Micheal I. Jordan
Learning and Relearning in Boltzmann Machines	45	(32)
G. E. Hinton
T. J. Sejnowski
Learning in Boltzmann Trees	77	(12)
Lawrence Saul
Michael I. Jordan
Deterministic Boltzmann Learning Performs Steepest Descent in Weight-Space	89	(8)
Geoffrey E. Hinton
Attractor Dynamics in Feedforward Neural Networks	97	(24)
Lawrence K. Saul
Michael I. Jordan
Efficient Learning in Boltzmann Machines Using Linear Response Theory	121	(20)
H. J. Kappen
F. B. Rodriguez
Asymmetric Parallel Boltzmann Machines Are Belief Networks	141	(4)
Radford M. Neal
Variational Learning in Nonlinear Gaussian Belief Networks	145	(22)
Brendan J. Frey
Geoffrey E. Hinton
Mixtures of Probabilistic Principal Component Analyzers	167	(40)
Michael E. Tipping
Christopher M. Bishop
Independent Factor Analysis	207	(50)
H. Attias
Hierarchical Mixtures of Experts and the EM Algorithm	257	(34)
Michael I. Jordan
Robert A. Jacobs
Hidden Neural Networks	291	(24)
Anders Krogh
Soren Kamaric Riis
Variational Learning for Switching State-Space Models	315	(34)
Zoubin Ghahramani
Geoffrey E. Hinton
Nonlinear Time-Series Prediction with Missing and Noisy Data	349	(18)
Volker Tresp
Reimar Hofmann
Correctness of Local Probability Propagation in Graphical Models with Loops	367	(42)
Yair Weiss
Index	409