Message-Passing Algorithms for Inference and Optimization“Belief Propagation” and “Divide and Concur”

Message-passing algorithms can solve a wide variety of optimization, inference, and constraint satisfaction problems. The algorithms operate on factor graphs that visually represent and specify the structure of the problems. After describing some of their applications, I survey the family of belief propagation (BP) algorithms, beginning with a detailed description of the min-sum algorithm and its exactness on tree factor graphs, and then turning to a variety of more sophisticated BP algorithms, including free-energy based BP algorithms, “splitting” BP algorithms that generalize “tree-reweighted” BP, and the various BP algorithms that have been proposed to deal with problems with continuous variables.