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# One-Shot Marginal MAP Inference in Markov Random Fields

*Proceedings of The 35th Uncertainty in Artificial Intelligence Conference*, PMLR 115:102-112, 2020.

#### Abstract

Statistical inference in Markov random fields (MRFs) is NP-hard in all but the simplest of cases. As a result, many algorithms, particularly in the case of discrete random variables, have been developed to perform approximate inference in practice. 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 flexible enough to handle both continuous and discrete random variables, efficient enough to be able to handle repeated statistical inferences, 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 the current approaches and demonstrate the efficacy of our approach on both synthetic models and real-world applications.