Kinetic interacting particle Langevin Monte Carlo
- 1Department of Mathematics, Imperial College London, Queen's Gate, SW7 2AZ London, UK
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.
Related
- Unbiased kinetic Langevin Monte Carlo with inexact gradients
- Persistence Pays: Square-root condition-number dependence for Metropolis-adjusted kinetic Langevin Monte Carlo with a non-reversibly updated accept/reject uniform
- Improved Guarantees for Langevin Monte Carlo with Average Smoothness
- A Kinetic Theory Approach To Ordered Fluids: Direct Simulation Monte Carlo Methods
- Parameter estimation in Conditional Sequential Monte Carlo algorithms through Particle Learning
BibTeX
@article{oliva2026kinetic,
title = {{Kinetic interacting particle Langevin Monte Carlo}},
author = {Paul Valsecchi Oliva and Ömer Deniz Akyıldız},
journal = {Statistics and Computing},
year = {2026},
month = sep,
doi = {10.1007/s11222-026-10980-z},
url = {https://doi.org/10.1007/s11222-026-10980-z},
note = {CC BY},
}
RIS
TY - JOUR
TI - Kinetic interacting particle Langevin Monte Carlo
AU - Paul Valsecchi Oliva
AU - Ömer Deniz Akyıldız
PY - 2026
DA - 2026/09/18
JO - Statistics and Computing
DO - 10.1007/s11222-026-10980-z
UR - https://doi.org/10.1007/s11222-026-10980-z
AB - 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.
SN - 0960-3174
SN - 1573-1375
ER -