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arXiv · 2510.13438

Near-Optimality of Contrastive Divergence Algorithms

Pierre Glaser·Kevin Han Huang·Arthur Gretton
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Abstract

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.

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Pierre Glaser, Kevin Han Huang, Arthur Gretton. 2025-10-15. Near-Optimality of Contrastive Divergence Algorithms. https://arxiv.org/abs/2510.13438

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