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Bethe free energy, Kikuchi approximations, and belief propagation algorithms

Date:
May 2001

MERL Contact: Jonathan Yedidia

Authors: Jonathan S. Yedidia, William T. Freeman, Yair Weiss

Abstract: This is an updated and expanded version of TR2000-26, but it is still in draft form. More importantly, our analysis lets us build on the progress made in statistical physics since Bethe's approximation was introduced in 1935. Kikuchi and others have shown how to construct more accurate free energy approximations, of which Bethe's approximation is the simplest. Exploiting the insights from our analysis, we derive generalized belief propagation (GBP) versions of these Kikuchi approximations. These new message passing algorithms can be significantly more accurate than ordinary BP, at an adjustable increase in complexity. We illustrate such a new GBP algorithm on a grid Markov network and show that it gives much more accurate marginal probabilities than those found using ordinary BP.

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