mlsanityData to 7 Oct 2026

Kinetic Interacting Particle Langevin Monte Carlo

arXiv 2407.05790 ↗First posted 8 Jul 2024stat.CO stat.MLcited by 7

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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.

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

Builds on

33 of 79 references.

References · 33

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
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  5. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  6. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  7. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  8. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  9. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
  10. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  11. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  12. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
21 more
  1. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  2. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  3. 2013Langevin diffusions and the Metropolis-adjusted Langevin algorithmcited by 29
  4. 2022Statistical exploration of the Manifold Hypothesiscited by 29
  5. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  6. 2016A consensus-based model for global optimization and its mean-field limitcited by 21
  7. 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
  8. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  9. 2020Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimizationcited by 13
  10. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  11. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  12. 2023Momentum Particle Maximum Likelihoodcited by 12
  13. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  14. 2019Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learningcited by 8
  15. 2024Proximal Interacting Particle Langevin Algorithmscited by 8
  16. 2020From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limitcited by 5
  17. 2014On perturbed proximal gradient algorithmscited by 4
  18. 2018Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimizationcited by 4
  19. 2021Statistical Finite Elements via Langevin Dynamicscited by 4
  20. 2023Gradient flows for empirical Bayes in high-dimensional linear modelscited by 4
  21. 2024Taming the Interacting Particle Langevin Algorithm: The Superlinear casecited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 3; 2026: 2.

7 papers.

  1. 2024Parallel Simulation for Log-concave Sampling and Score-based Diffusion Modelscited by 6
  2. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  3. 2025Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithmcited by 3
  4. 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 3
  5. 2024Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequalitycited by 1
  6. 2026Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimationcited by 0
  7. 2026Particle-based Generalised Stochastic Optimisationcited by 0