Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Oliva, Paul Felix Valsecchi, Akyildiz, O. Deniz, Duncan, Andrew
Institution: Imperial College London
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414819805
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