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Traditional learning methods for training Markov random fields require doinginference over all variables to compute the likelihood gradient. The iterationcomplexity for those methods therefore scales with the size of the graphicalmodels. In this paper, we propose \emph{block belief propagation learning}(BBPL), which uses block-coordinate updates of approximate marginals to computeapproximate gradients, removing the need to compute inference on the entiregraphical model. Thus, the iteration complexity of BBPL does not scale with thesize of the graphs. We prove that the method converges to the same solution asthat obtained by using full inference per iteration, despite theseapproximations, and we empirically demonstrate its scalability improvementsover standard training methods.

Block Belief Propagation for Parameter Learning in Markov Random Fields