# A fast non-reversible sampler for Bayesian mixture models

arXiv: https://arxiv.org/abs/2510.03226 · HTML: https://mlsanity.com/paper/2510.03226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [On the Computational Complexity of High-Dimensional Bayesian Variable Selection](https://mlsanity.com/paper/1505.07925/) (2015)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much](https://mlsanity.com/paper/1606.03432/) (2016)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [Lifting -- A nonreversible Markov chain Monte Carlo Algorithm](https://mlsanity.com/paper/1412.8762/) (2014)
- [An asymptotic Peskun ordering and its application to lifted samplers](https://mlsanity.com/paper/2003.05492/) (2020)
- [Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs](https://mlsanity.com/paper/2310.05655/) (2023)
- [Simple conditions for convergence of sequential Monte Carlo genealogies with applications](https://mlsanity.com/paper/2007.00096/) (2020)
- [Comparison Theorems for the Mixing Times of Systematic and Random Scan Dynamics](https://mlsanity.com/paper/2410.11136/) (2024)

## Abstract (arXiv)

Mixtures models are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to converge when the number of observations n is large. In this paper we introduce a novel and simple non-reversible sampling scheme for Bayesian mixture models (with fixed or varying number of components), which is shown to drastically outperform classical samplers in many scenarios of interest, especially during convergence phase and when components in the mixture have non-negligible overlap. At the theoretical level, we show that the performance of the proposed non-reversible scheme cannot be worse than the standard one, in terms of asymptotic variance, by more than a factor of four; and we provide a scaling limit analysis suggesting that the non-reversible sampler can reduce the convergence time from O(n2) to O(n). We also discuss why the statistical features of mixture models make them an ideal case for the use of non-reversible discrete samplers.