I thought readers of sci.stat.edu might be interested in this book. For
more information please visit
http://mitpress.mit.edu/catalog/item/default.asp?sid=5CEC3656-296C-4C48-B6E3-6BDFAC7EBADD&ttype=2&tid=3847
Advanced Mean Field Methods
Theory and Practice
edited by Manfred Opper and David Saad
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.
Manfred Opper is a Reader and David Saad is Professor, the Neural
Computing Research Group, School of Engineering and Applied Science,
Aston University, UK.
7 x 10, 300 pp.
cloth ISBN 0-262-15054-9
Neural Information Processing series
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