MAP estimation in Binary MRFs via Bipartite Multi-cuts

We propose a new LP relaxation for obtaining the MAP assignment of a binary MRF with pairwise potentials. Our relaxation is derived from reducing the MAP assignment problem to an instance of a recently proposed Bipartite Multi-cut problem where the LP relaxation is guaranteed to provide an O(log k) approximation where k is the number of vertices adjacent to non-submodular edges in the MRF. We then propose a combinatorial algorithm to efficiently solve the LP and also provide a lower bound by concurrently solving its dual to within an ɛ approximation. The algorithm is up to an order of magnitude faster and provides better MAP scores and bounds than the state of the art message passing algorithm of [1] that tightens the local marginal polytope with third-order marginal constraints.