# Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models

arXiv: https://arxiv.org/abs/2604.26029 · HTML: https://mlsanity.com/paper/2604.26029/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 13 of 13)

- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [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)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [The promises and pitfalls of Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1811.10072/) (2018)
- [Stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/1907.06986/) (2019)
- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Efficiently Solving MDPs with Stochastic Mirror Descent](https://mlsanity.com/paper/2008.12776/) (2020)
- [The Mirror Langevin Algorithm Converges with Vanishing Bias](https://mlsanity.com/paper/2109.12077/) (2021)
- [Control Variates for Stochastic Gradient MCMC](https://mlsanity.com/paper/1706.05439/) (2017)
- [Policy Optimization with Stochastic Mirror Descent](https://mlsanity.com/paper/1906.10462/) (2019)
- [Scalable and Calibrated Sampling for Bayesian Generalized Linear Mixed Model via Stochastic Gradient Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.03007/) (2024)

## Built on by (most cited first, 1 of 1)

- [Integrating Neural Encoders in Bayesian Generalized Linear Mixed Models for Multimodal Data](https://mlsanity.com/paper/2607.04647/) (2026)

## Abstract (arXiv)

We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces divergent Markov chains and cannot be reliably used for sampling covariance parameters of random effects. We advocate the use of a mirror Langevin dynamics algorithm, propose the novel stochastic mirror Langevin dynamics based on data subsampling, and provide concrete guidelines for its use in a Bayesian inference framework. Based on an explicit Wasserstein distance error bound between the posterior and its algorithmic approximation, we propose a post-processing step that yields an asymptotic, order-wise correct estimation of the posterior variance, eliminating the irreducible posterior variance estimation bias due to subsampling. Empirical performance of the method is evaluated through simulated experiments and a longitudinal study of pain trajectories in a study of breast cancer survivors.