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Conference Proceeding Article

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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

Research Areas

Intelligent Systems and Decision Analytics


International Conference on Artificial Intelligence and Statistics (AISTATS)



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