mlsanityData to 14 Oct 2026

Proximal Interacting Particle Langevin Algorithms

arXiv 2406.14292 ↗First posted 20 Jun 2024stat.CO math.OC stat.MLcited by 8

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Abstract (arXiv)

We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov chain Monte Carlo techniques and interacting particle Langevin algorithms, we propose three algorithms tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove nonasymptotic bounds for the parameter estimates produced by the different algorithms in the strongly log-concave setting and provide comprehensive numerical experiments on various models to demonstrate the effectiveness of the proposed methods. In particular, we demonstrate the utility of our family of algorithms for sparse Bayesian logistic regression, training of sparse Bayesian neural networks or neural networks with non-differentiable activation functions, image deblurring, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 33 of its 84 references that are in the map. First posted on arXiv 20 Jun 2024.

Builds on

33 of 84 references.

References · 33

  1. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  2. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  3. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  4. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  5. 2017On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learningcited by 142
  6. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
  7. 2015Practical Bayesian model evaluation using leave-one-out cross-validation and WAICcited by 110
  8. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 86
  9. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  10. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  11. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  12. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 45
21 more
  1. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
  2. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  3. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
  4. 2020Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriorscited by 29
  5. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  6. 2019Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Ratescited by 17
  7. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  8. 2020Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimizationcited by 13
  9. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  10. 2023Momentum Particle Maximum Likelihoodcited by 12
  11. 2023Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Bettingcited by 11
  12. 2023Subgradient Langevin Methods for Sampling from Non-smooth Potentialscited by 11
  13. 2014Modular proximal optimization for multidimensional total-variation regularizationcited by 10
  14. 2022Trace norm regularization for multi-task learning with scarce datacited by 10
  15. 2014Estimating Traffic and Anomaly Maps via Network Tomographycited by 6
  16. 2021Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-Differentiable Priorscited by 6
  17. 2024Stochastic Approximation with Biased MCMC for Expectation Maximizationcited by 5
  18. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4
  19. 2024Adaptive proximal gradient methods are universal without approximationcited by 4
  20. 2024Taming the Interacting Particle Langevin Algorithm: The Superlinear casecited by 3
  21. 2024GD doesn't make the cut: Three ways that non-differentiability affects neural network trainingcited by 2

Built on by

Cited by year (2026 to 14 Oct)

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

8 papers.

  1. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  2. 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 5
  3. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  4. 2025Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithmcited by 3
  5. 2024Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequalitycited by 1
  6. 2026Efficient Stochastic Optimisation via Sequential Monte Carlocited by 1
  7. 2026Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimationcited by 0
  8. 2026Particle-based Generalised Stochastic Optimisationcited by 0