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Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms (2005)

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by Jonathan S. Yedidia , William T. Freeman , Yair Weiss
Venue:IEEE Transactions on Information Theory
Citations:584 - 13 self
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BibTeX

@ARTICLE{Yedidia05constructingfree,
    author = {Jonathan S. Yedidia and William T. Freeman and Yair Weiss},
    title = {Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms},
    journal = {IEEE Transactions on Information Theory},
    year = {2005},
    volume = {51},
    pages = {2282--2312}
}

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Abstract

Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxent-normal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a region-based approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.

Keyphrases

free energy approximation    factor graph    generalized belief propagation algorithm    bethe approximation    artificial intelligence    region-based approximation    point correspond    statistical physic    region graph method    important inference problem    efficient way    stationary point    regionbased free energy approximation    free energy    empirical result    error-correcting coding theory    maxent-normal approximation    bethe method    corresponding gbp algorithm    belief propagation    cluster variation method    generalized belief propagation    different method    junction graph method    valid approximation    computer vision    marginal probability   

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