Near-Optimality of Contrastive Divergence Algorithms

• URL: http://arxiv.org/abs/2510.13438v1
• Date: Wed, 15 Oct 2025 11:35:58 GMT
• Title: Near-Optimality of Contrastive Divergence Algorithms
• Authors: Pierre Glaser, Kevin Han Huang, Arthur Gretton,
• Abstract summary: We show that the CD algorithm can achieve the parametric rate $O(n-1 / 2)$.<n>We additionally show that CD can be near-optimal, in the sense that its variance is close to the Cram'er-Rao lower bound.
• Score: 22.499181350622617
• License: http://creativecommons.org/licenses/by/4.0/
• 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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