Message-Passing Algorithms for MAP Estimation Using DC Programming

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 concaveconvex procedure (CCCP) to develop efficient message-passing solvers. The resulting algorithms are guaranteed to converge to a global optimum of the well-studied local 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 useful 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 nearoptimal solutions for standard benchmarks.

• Type: Journal
• Year: 2012
• Where: JMLR
• Authors: Akshat Kumar, Shlomo Zilberstein, Marc Toussaint
• Keywords: Convex Functions, JMLR 2012, Linear Programming Formulation, Outer Bound, Programming Languages