Kinetic interacting particle Langevin Monte Carlo
File(s)
Pubished version
Author(s)
Valsecchi Oliva, Paul
Akyildiz, O Deniz
Type
Journal Article
Abstract
This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process that evolves jointly in the space of parameters and latent variables and show that the stationary distribution of this diffusion concentrates around the maximum marginal likelihood estimate of the parameters. We then provide two explicit discretisations of this diffusion as practical algorithms to estimate parameters of statistical models. For each algorithm, we obtain nonasymptotic rates of convergence in Wasserstein-2 distance for the case where the joint log-likelihood is strongly concave with respect to latent variables and parameters. We achieve accelerated convergence rates clearly demonstrating improvement in dimension dependence. To demonstrate the utility of the introduced methodology, we provide numerical experiments that illustrate the effectiveness of the proposed diffusion for statistical inference. Our setting covers a broad number of applications, including unsupervised learning, statistical inference, and inverse problems.
Date Issued
2026-10-01
Date Acceptance
2026-09-04
Citation
Statistics and computing, 2026, 36 (5)
ISSN
0960-3174
Publisher
Springer
Journal / Book Title
Statistics and computing
Volume
36
Issue
5
Copyright Statement
© The Author(s) 2026.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/42763452
PII: 10980
Subjects
Interacting particle Langevin algorithms
Maximum marginal likelihood estimation
Parameter inference in latent variable models
Publication Status
Published
Coverage Spatial
United States
Article Number
221
Date Publish Online
2026-09-18