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Loop Calculus in Statistical Physics and Information Science

Michael Chertkov·Vladimir Y. Chernyak
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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.

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Michael Chertkov, Vladimir Y. Chernyak. 2006-03-08. Loop Calculus in Statistical Physics and Information Science. https://doi.org/10.1103/physreve.73.065102

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