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# Contrastive Divergence Learning with Chained Belief Propagation

*Proceedings of the 10th International Conference on Probabilistic Graphical Models*, PMLR 138:161-172, 2020.

#### Abstract

Contrastive Divergence (CD) is an important maximum-likelihood learning approach for probabilistic graphical models. CD maximizes the difference in likelihood between the observed data and those sampled from the current model distribution using Markov Chain Monte Carlo (MCMC). Nevertheless, the overall performance of CD is hampered by the slow mixing rate of MCMC in the presence of combinatorial constraints. A competing approach BP-CD replaces MCMC with Belief Propagation (BP). However, their samples are generated from a mean-field
approximation, which may be far away from the true distribution. Here we propose contrastive divergence learning with chained belief propagation (BPChain-CD). To generate one sample in CD, we fix one variable at a time based on the marginal distribution computed by BP conditioned on previous variables. We analyze BPChain-CD both theoretically and experimentally. We show that BPChain-CD learns better models compared with BP-CD and CD on a range of maximum-likelihood learning experiments.