Loop Calculus in Statistical Physics and Information Science
Statistical Mechanics
2009-11-11 v2 Disordered Systems and Neural Networks
Information Theory
math.IT
Abstract
Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP contribution, the rest are expressed as loop-contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed.
Keywords
Cite
@article{arxiv.cond-mat/0601487,
title = {Loop Calculus in Statistical Physics and Information Science},
author = {Michael Chertkov and Vladimir Y. Chernyak},
journal= {arXiv preprint arXiv:cond-mat/0601487},
year = {2009}
}
Comments
4 pages, submitted to Phys.Rev.Lett. Changes: More general model, Simpler derivation