Uniform-in-time convergence bounds for Persistent Contrastive Divergence algorithms

Abstract:We propose a continuous-time formulation of a noisy persistent contrastive divergence (PCD)-like method for maximum likelihood estimation (MLE) of unnormalised densities. Our approach couples parameter updates and sampling of the parametrised density in a multiscale system of stochastic differential equations (SDEs). From this formulation, we derive non-asymptotic bounds for weak test-function errors between the resulting numerical schemes and the MLE point target. The error is decomposed into numerical discretisation, slow-fast averaging, and finite-temperature concentration terms. We also introduce an efficient implementation based on explicit stabilized integrators and establish corresponding long-time error estimates. This leads to a novel method for training energy-based models (EBMs) with quantitative error guarantees.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2510.01944 [stat.ML]

(or arXiv:2510.01944v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2510.01944 Focus to learn more arXiv-issued DOI via DataCite

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