2013/05/17 by Andrew E. Gelfand, Andrew Gelfand, Gelfand, Andrew +4 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Bayesian Modeling and Causal Inference #DNA and Biological Computing #Error Correcting Code Techniques #cs.AI #cs.DS
paper · pdf · doi:10.48550/arxiv.1305.4130
To appear in ISIT 2013
arxiv created 2013/05/17 · arxiv updated 2013/05/20
Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve a special class of Linear Programming (LP) problems. For this class of problems, MAP inference can be stated as an integer LP with an LP relaxation that coincides with minimization of the BFE at ``zero temperature". We generalize these prior results and establish a tight characterization of the LP problems that can be formulated as an equivalent LP relaxation of MAP inference. Moreover, we suggest an efficient, iterative annealing BP algorithm for solving this broader class of LP problems. We demonstrate the algorithm's performance on a set of weighted matching problems by using it as a cutting plane method to solve a sequence of LPs tightened by adding ``blossom'' inequalities.