Multilevel Belief Propagation for Fast Inference on Markov Random Fields

Graph-based inference plays an important role in many mining and learning tasks. Among all the solvers for this problem, belief propagation (BP) provides a general and efficient way to derive approximate solutions. However, for large scale graphs the computational cost of BP is still demanding. In this paper, we propose a multilevel algorithm to accelerate belief propagation on Markov Random Fields (MRF). First, we coarsen the original graph to get a smaller one. Then, BP is applied on the new graph to get a coarse result. Finally the coarse solution is efficiently refined back to derive the original solution. Unlike traditional multi- resolution approaches, our method features adaptive coarsening and efficient refinement. The above process can be recursively applied to reduce the computational cost remarkably. We theoretically justify the feasibility of our method on Gaussian MRFs, and empirically show that it is also effectual on discrete MRFs. The effectiveness of our method is verified in experiments on various inference tasks.