# Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm

arXiv: https://arxiv.org/abs/2505.18427 · HTML: https://mlsanity.com/paper/2505.18427/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 60 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 20 of 20)

- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Large Language Models Are Latent Variable Models: Explaining and Finding Good Demonstrations for In-Context Learning](https://mlsanity.com/paper/2301.11916/) (2023)
- [A Guide Through the Zoo of Biased SGD](https://mlsanity.com/paper/2305.16296/) (2023)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [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)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Efficient Training of Energy-Based Models Using Jarzynski Equality](https://mlsanity.com/paper/2305.19414/) (2023)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [Convergence rates for optimised adaptive importance samplers](https://mlsanity.com/paper/1903.12044/) (2019)
- [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)
- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization](https://mlsanity.com/paper/2503.15704/) (2025)
- [Non-asymptotic Analysis of Biased Adaptive Stochastic Approximation](https://mlsanity.com/paper/2402.02857/) (2024)
- [Stochastic Approximation with Biased MCMC for Expectation Maximization](https://mlsanity.com/paper/2402.17870/) (2024)
- [A mirror descent approach to maximum likelihood estimation in latent variable models](https://mlsanity.com/paper/2501.15896/) (2025)
- [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025)

## Built on by (most cited first, 3 of 3)

- [Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics](https://mlsanity.com/paper/2510.12311/) (2025)
- [Efficient Stochastic Optimisation via Sequential Monte Carlo](https://mlsanity.com/paper/2601.22003/) (2026)
- [Particle-based Generalised Stochastic Optimisation](https://mlsanity.com/paper/2608.02844/) (2026)

## Abstract (arXiv)

We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski's equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods - an uncommon feature among scalable methods - makes our approach particularly suited for model selection, which we validate through dedicated experiments.