One-Shot Marginal MAP Inference in Markov Random Fields

Statistical inference in Markov random fields (MRFs) is NP-hard in all but the simplest cases. As a result, many algorithms, particularly in the case of discrete random variables, have been developed to perform approximate inference. However, most of these methods scale poorly, cannot be applied to continuous random variables, or are too slow to be used in situations that call for repeated statistical inference on the same model. In this work, we propose a novel variational inference strategy that is efficient for repeated inference tasks, flexible enough to handle both continuous and discrete random variables, and scalable enough, via modern GPUs, to be practical on MRFs with hundreds of thousands of random variables. We prove that our approach overcomes weaknesses of existing ones and demonstrate its efficacy on both synthetic models and real-world applications.