Parallelization of Minimum Probability Flow on Binary Markov Random Fields

We introduce a parallelized version of the minimum probability flow algorithm for learning the parametrization of pairwise Markov random fields. Our algorithm is embarrassingly parallel over arbitrary subgraphs, making it a useful alternative to direct approaches when an underlying structure of the graph is known. Unlike competing parallel approaches, the objective function for learning the parameters of a Markov random field is convex and efficiently solvable using a gradient descent method. We present a theory that explains why factorizing a graph can lead to computational tractability without sacrificing much estimator performance and show results for learning the parameters of binary Markov random fields. We compare the efficiency of minimum probability flow to maximum likelihood on tractable Markov random fields and present wall-clock estimation times for both approaches.