# Kinetic Interacting Particle Langevin Monte Carlo

arXiv: https://arxiv.org/abs/2407.05790 · HTML: https://mlsanity.com/paper/2407.05790/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 79 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 30 of 33)

- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Sharp convergence rates for Langevin dynamics in the nonconvex setting](https://mlsanity.com/paper/1805.01648/) (2018)
- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization](https://mlsanity.com/paper/1910.02008/) (2019)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration](https://mlsanity.com/paper/1809.04618/) (2018)
- [Langevin diffusions and the Metropolis-adjusted Langevin algorithm](https://mlsanity.com/paper/1309.2983/) (2013)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [A consensus-based model for global optimization and its mean-field limit](https://mlsanity.com/paper/1604.05648/) (2016)
- [Fully probabilistic deep models for forward and inverse problems in parametric PDEs](https://mlsanity.com/paper/2208.04856/) (2022)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization](https://mlsanity.com/paper/2002.05465/) (2020)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case](https://mlsanity.com/paper/2301.08039/) (2023)
- [Momentum Particle Maximum Likelihood](https://mlsanity.com/paper/2312.07335/) (2023)
- [Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting](https://mlsanity.com/paper/2305.14916/) (2023)
- [Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learning](https://mlsanity.com/paper/1903.10328/) (2019)
- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit](https://mlsanity.com/paper/2012.05613/) (2020)
- [On perturbed proximal gradient algorithms](https://mlsanity.com/paper/1402.2365/) (2014)
- [Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization](https://mlsanity.com/paper/1811.09469/) (2018)

## Built on by (most cited first, 7 of 7)

- [Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models](https://mlsanity.com/paper/2412.07435/) (2024)
- [Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics](https://mlsanity.com/paper/2510.12311/) (2025)
- [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025)
- [Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm](https://mlsanity.com/paper/2505.18427/) (2025)
- [Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality](https://mlsanity.com/paper/2407.17949/) (2024)
- [Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2603.08676/) (2026)
- [Particle-based Generalised Stochastic Optimisation](https://mlsanity.com/paper/2608.02844/) (2026)

## Abstract (arXiv)

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.