Restricted Boltzmann machines~(RBMs) and conditional RBMs~(CRBMs) are popular models for a wide range of applications. In previous work, learning on such models has been dominated by contrastive divergence~(CD) and its variants. Belief propagation~(BP) algorithms are believed to be slow for structured prediction on conditional RBMs~(e.g., Mnih et al. [2011]), and not as good as CD when applied in learning~(e.g., Larochelle et al. [2012]). In this work, we present a matrix-based implementation of belief propagation algorithms on CRBMs, which is easily scalable to tens of thousands of visible and hidden units. We demonstrate that, in both maximum likelihood and max-margin learning, training conditional RBMs with BP as the inference routine can provide significantly better results than current state-of-the-art CD methods on structured prediction problems. We also include practical guidelines on training CRBMs with BP, and some insights on the interaction of learning and inference algorithms for CRBMs.
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