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Inference problems in graphical models can be represented as a constrainedoptimization of a free energy function. It is known that when the Bethe freeenergy is used, the fixedpoints of the belief propagation (BP) algorithmcorrespond to the local minima of the free energy. However BP fails to convergein many cases of interest. Moreover, the Bethe free energy is non-convex forgraphical models with cycles thus introducing great difficulty in derivingefficient algorithms for finding local minima of the free energy for generalgraphs. In this paper we introduce two efficient BP-like algorithms, onesequential and the other parallel, that are guaranteed to converge to theglobal minimum, for any graph, over the class of energies known as "convex freeenergies". In addition, we propose an efficient heuristic for setting theparameters of the convex free energy based on the structure of the graph.

Convergent Message-Passing Algorithms for Inference over General Graphs with Convex Free Energies