Near-Optimality of Contrastive Divergence Algorithms

We perform a non-asymptotic analysis of the contrastive divergence (CD) algorithm, a training method for unnormalized models. While prior work has established that (for exponential family distributions) the CD iterates asymptotically converge at an O(n-1 / 3) rate to the true parameter of the data distribution, we show, under some regularity assumptions, that CD can achieve the parametric rate O(n-1 / 2). Our analysis provides results for various data batching schemes, including the fully online and minibatch ones. We additionally show that CD can be near-optimal, in the sense that its asymptotic variance is close to the Cram'er-Rao lower bound.