Message Passing Algorithms for MAP Estimation Using DC Programming
Akshat Kumar, Shlomo Zilberstein, Marc Toussaint · 2012
We address the problem of finding the most likely assignment or MAP estimation in a Markov random field. We analyze the linear programming formulation of MAP through the lens of difference of convex functions (DC) programming, and use the concave-convex procedure (CCCP) to develop effi-cient message-passing solvers. The result-ing algorithms are guaranteed to converge to a global optimum of the well-studied lo-cal polytope, an outer bound on the MAP marginal polytope. To tighten the outer bound, we show how to combine it with the mean-field based inner bound and, again, solve it using CCCP. We also identify a use-ful relationship between the DC formulations and some recently proposed algorithms based on Bregman divergence. Experimentally, this hybrid approach produces optimal solutions for a range of hard OR problems and near-optimal solutions for standard benchmarks. 1