# Proximal Interacting Particle Langevin Algorithms

arXiv: https://arxiv.org/abs/2406.14292 · HTML: https://mlsanity.com/paper/2406.14292/

## 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 (most cited first, 30 of 33)

- [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)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [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)
- [Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Space](https://mlsanity.com/paper/2304.05398/) (2023)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates](https://mlsanity.com/paper/1905.11768/) (2019)
- [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)
- [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)
- [Subgradient Langevin Methods for Sampling from Non-smooth Potentials](https://mlsanity.com/paper/2308.01417/) (2023)
- [Modular proximal optimization for multidimensional total-variation regularization](https://mlsanity.com/paper/1411.0589/) (2014)
- [Trace norm regularization for multi-task learning with scarce data](https://mlsanity.com/paper/2202.06742/) (2022)
- [Estimating Traffic and Anomaly Maps via Network Tomography](https://mlsanity.com/paper/1407.1660/) (2014)
- [Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-Differentiable Priors](https://mlsanity.com/paper/2103.09017/) (2021)
- [Stochastic Approximation with Biased MCMC for Expectation Maximization](https://mlsanity.com/paper/2402.17870/) (2024)
- [Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling](https://mlsanity.com/paper/2308.09460/) (2023)

## Built on by (most cited first, 8 of 8)

- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (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)
- [Efficient Stochastic Optimisation via Sequential Monte Carlo](https://mlsanity.com/paper/2601.22003/) (2026)
- [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)

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.