Kinetic Interacting Particle Langevin Monte Carlo

arXiv stat.ML / 4/17/2026

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Key Points

The paper proposes Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods that use an interacting underdamped Langevin diffusion for statistical inference in latent variable models.
It constructs a joint diffusion over both model parameters and latent variables and proves that its stationary distribution concentrates around the maximum marginal likelihood estimate of the parameters.
The authors introduce two practical discretization schemes of the diffusion and provide non-asymptotic convergence rates in Wasserstein-2 distance under strong concavity assumptions.
The results show accelerated convergence with improved dependence on problem dimension, supported by numerical experiments across unsupervised learning, statistical inference, and inverse problems.

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.