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We consider the energy minimization problem for undirected graphical models,also known as MAP-inference problem for Markov random fields which is NP-hardin general. We propose a novel polynomial time algorithm to obtain a part ofits optimal non-relaxed integral solution. Our algorithm is initialized withvariables taking integral values in the solution of a convex relaxation of theMAP-inference problem and iteratively prunes those, which do not satisfy ourcriterion for partial optimality. We show that our pruning strategy is in acertain sense theoretically optimal. Also empirically our method outperformsprevious approaches in terms of the number of persistently labelled variables.The method is very general, as it is applicable to models with arbitraryfactors of an arbitrary order and can employ any solver for the consideredrelaxed problem. Our method's runtime is determined by the runtime of theconvex relaxation solver for the MAP-inference problem.

Partial Optimality by Pruning for MAP-Inference with General Graphical Models