Conference Proceeding Article
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 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.
Artificial Intelligence and Robotics | Business | Operations Research, Systems Engineering and Industrial Engineering
Intelligent Systems and Decision Analytics
International Conference on Artificial Intelligence and Statistics (AISTATS)
KUMAR, Akshat; Zilberstein, S.; and Toussaint, M..
Message Passing Algorithms for MAP Estimation Using DC Programming. (2012). International Conference on Artificial Intelligence and Statistics (AISTATS). 22, 656-664. Research Collection School Of Information Systems.
Available at: http://ink.library.smu.edu.sg/sis_research/2203