Partial Optimality by Pruning for MAP-Inference with General Graphical
  Models
  We consider the energy minimization problem for undirected graphical models,
also known as MAP-inference problem for Markov random fields which is NP-hard
in general. We propose a novel polynomial time algorithm to obtain a part of
its optimal non-relaxed integral solution. Our algorithm is initialized with
variables taking integral values in the solution of a convex relaxation of the
MAP-inference problem and iteratively prunes those, which do not satisfy our
criterion for partial optimality. We show that our pruning strategy is in a
certain sense theoretically optimal. Also empirically our method outperforms
previous approaches in terms of the number of persistently labelled variables.
The method is very general, as it is applicable to models with arbitrary
factors of an arbitrary order and can employ any solver for the considered
relaxed problem. Our method's runtime is determined by the runtime of the
convex relaxation solver for the MAP-inference problem.
