LP relaxation based message passing and flow-based algorithms are two of the popular techniques for performing MAP inference in graphical models. Generic Cuts (GC) (Arora et al., 2015) combines the two approaches to generalize the traditional max-flow min-cut based algorithms for binary models with higher order clique potentials. The algorithm has been shown to be significantly faster than the state of the art algorithms. The time and memory complexities of Generic Cuts are linear in the number of constraints, which in turn is exponential in the clique size. This limits the applicability of the approach to small cliques only. In this paper, we propose a lazy version of Generic Cuts exploiting the property that in most of such inference problems a large fraction of the constraints are never used during the course of minimization. We start with a small set of constraints (called the active constraints) which are expected to play a role during the minimization process. GC is then run with this reduced set allowing it to be efficient in time and memory. The set of active constraints is adaptively learnt over multiple iterations while guaranteeing convergence to the optimum for submodular clique potentials. Our experiments show that the number of constraints required by the algorithm is typically less than 3% of the total number of constraints. Experiments on computer vision datasets show that our approach can significantly outperform the state of the art both in terms of time and memory and is scalable to clique sizes that could not be handled by existing approaches. 
Lazy Generic Cuts