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