  Contrastive divergence (CD) is a promising method of inference in high
dimensional distributions with intractable normalizing constants, however, the
theoretical foundations justifying its use are somewhat shaky. This document
proposes a framework for understanding CD inference, how/when it works, and
provides multiple justifications for the CD moment conditions, including
framing them as a variational approximation. Algorithms for performing
inference are discussed and are applied to social network data using an
exponential-family random graph models (ERGM). The framework also provides
guidance about how to construct MCMC kernels providing good CD inference, which
turn out to be quite different from those used typically to provide fast global
mixing.
