# Near-Optimality of Contrastive Divergence Algorithms

arXiv: https://arxiv.org/abs/2510.13438 · HTML: https://mlsanity.com/paper/2510.13438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2025.

## Abstract (arXiv)

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.