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Contrastive divergence (CD) is a promising method of inference in highdimensional distributions with intractable normalizing constants, however, thetheoretical foundations justifying its use are somewhat shaky. This documentproposes a framework for understanding CD inference, how/when it works, andprovides multiple justifications for the CD moment conditions, includingframing them as a variational approximation. Algorithms for performinginference are discussed and are applied to social network data using anexponential-family random graph models (ERGM). The framework also providesguidance about how to construct MCMC kernels providing good CD inference, whichturn out to be quite different from those used typically to provide fast globalmixing.

Why (and When and How) Contrastive Divergence Works