Advanced Mean Field Methods: Theory and Practice by Manfred Opper, David Saad

By Manfred Opper, David Saad

A big challenge in glossy probabilistic modeling is the large computational complexity fascinated with normal calculations with multivariate chance distributions whilst the variety of random variables is huge. simply because distinct computations are infeasible in such instances and Monte Carlo sampling ideas could succeed in their limits, there's a desire for tactics that permit for effective approximate computations. one of many easiest approximations relies at the suggest box approach, which has a protracted heritage in statistical physics. the strategy is customary, rather within the turning out to be box of graphical models.Researchers from disciplines reminiscent of statistical physics, computing device technological know-how, and mathematical information are learning how you can increase this and comparable equipment and are exploring novel software parts. prime methods contain the variational strategy, which works past factorizable distributions to accomplish systematic advancements; the faucet (Thouless-Anderson-Palmer) method, which contains correlations by way of together with potent response phrases within the suggest box conception; and the extra common tools of graphical models.Bringing jointly principles and methods from those varied disciplines, this publication covers the theoretical foundations of complicated suggest box tools, explores the relation among the various methods, examines the standard of the approximation got, and demonstrates their software to numerous parts of probabilistic modeling.

Show description

Read or Download Advanced Mean Field Methods: Theory and Practice PDF

Similar mathematical physics books

Selected papers of Morikazu Toda

This quantity includes chosen papers of Dr Morikazu Toda. The papers are prepared in chronological order of publishing dates. between Dr Toda's many contributions, his works on beverages and nonlinear lattice dynamics could be pointed out. The one-dimensional lattice the place nearest neighboring debris engage via an exponential capability is termed the Toda lattice that's a miracle and certainly a jewel in theoretical physics.

Solution of Initial Value Problems in Classes of Generalized Analytic Functions

The aim of the current e-book is to resolve preliminary price difficulties in periods of generalized analytic services in addition to to provide an explanation for the functional-analytic historical past fabric intimately. From the viewpoint of the idea of partial differential equations the e-book is intend­ ed to generalize the classicalCauchy-Kovalevskayatheorem, while the functional-analytic historical past attached with the strategy of successive approximations and the contraction-mapping precept results in the con­ cept of so-called scales of Banach areas: 1.

Additional resources for Advanced Mean Field Methods: Theory and Practice

Sample text

Phys. Rev. 81, 988, 1951. , Special issue in honor of R. Kikuchi, Prog. Theor. Phys. , 115, 1994. , IEEE Trans. on Inf. Theory, 1999. C. , IEEE J. on Sel Areas in Comm. 16 ( 2 ) , 140, 1998. , Parisi G. , Spin Glass Theory and Beyond, Singapore: World Scientific, 1987. , Physica 98A, 566, 1979. , Weiss Y. , in Proc. Uncertainty in AI, 1999. [22] Parisi G. , J. Phys. A 28, 5267, 1995. , Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, San Francisco: Morgan Kaufman, 1988.

22,2181 (1989). [15lMezard M. ,Mean Field Theory of Randomly Frustrated Systems with Finite Connectivity, Europhys. Lett. 3,1067 (1987). ,Parisi G. and Virasoro M. ,Europhys. Lett. 1,77 (1986) and Spin Glass Theory and Beyond, Lecture Notes in Physics, 9,World Scientific (1987). [17lNemoto K. ,J. Phys. C 18,L529 (1985). [18l0pper M. ,this book. ,Statistical Field Theory, Addison Wesley,Reading Massachusetts (1988). [20lParisi G. ,Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices,J.

Before, we work out the mean field approximations for the general case, we first illustrate this idea for Boltzmann distributions in section 3. Subsequently, in section 4 we consider the general case. Finally, in section 5 we illustrate the approach for sigmoid belief networks. 2 Mean field theory In this section we consider a form of mean field theory that was previously proposed by Plefka [13] for Boltzmann-Gibbs distributions. It turns out, however, that the restriction to Boltzmann-Gibbs distributions is not necessary and one can derive results that are valid for arbitrary probability distributions.

Download PDF sample

Rated 4.86 of 5 – based on 44 votes