Advanced Mean Field Methods: Theory and Practice (Neural Information Processing) - Hardcover

Hardcover

ISBN 10: 0262150549 ISBN 13: 9780262150545

Publisher: Bradford Books, 2001

Synopsis

This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models.

Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models.

Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

About this title

About the Author:

Manfred Opper is a Reader at the Neural Computing Research Group, School of Engineering and Applied Science, Aston University, UK.

Review:

This book provides an extremely valuable treatment of mean field methods and their application to problems in probabilistic inference and learning.

(Lawrence Saul, Principal Technical Staff Member, AT&T Labs -- Research)

About this edition

• Publisher: Bradford Books
• Publication date: 2001
• ISBN 10: 0262150549
• ISBN 13: 9780262150545
• Binding: Hardcover
• Number of pages: 300
• Editor: Opper Manfred, Saad David