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A New Class of Upper Bounds on the Log Partition Function

2005
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IEEE Transactions on Information Theory
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We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from convex duality and information geometry: in particular, it exploits mixtures of distributions in the exponential domain, and the Legendre

doi:10.1109/tit.2005.850091
fatcat:gj3suuqbcnawdlaipub25a7jt4