# Fast sampling and model selection for Bayesian mixture models

arXiv: https://arxiv.org/abs/2501.07668 · HTML: https://mlsanity.com/paper/2501.07668/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 67 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Estimating the number of communities in a network](https://mlsanity.com/paper/1605.02753/) (2016)
- [Overfitting Bayesian Mixture Models with an Unknown Number of Components](https://mlsanity.com/paper/1502.05427/) (2015)
- [Consistency of community structure in complex networks](https://mlsanity.com/paper/1908.09867/) (2019)
- [Representative community divisions of networks](https://mlsanity.com/paper/2105.04612/) (2021)
- [Distributed Collapsed Gibbs Sampler for Dirichlet Process Mixture Models in Federated Learning](https://mlsanity.com/paper/2312.11169/) (2023)
- [Exploring Network Structure with the Density of States](https://mlsanity.com/paper/2410.18253/) (2024)

## Built on by (most cited first, 2 of 2)

- [Mixture models for data with unknown distributions](https://mlsanity.com/paper/2502.19605/) (2025)
- [Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Models](https://mlsanity.com/paper/2608.20183/) (2026)

## Abstract (arXiv)

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is commonly done. Some previous authors have found the former approach to have slow mixing, but we show that, implemented correctly, it can achieve excellent performance. In particular, we describe a new Monte Carlo algorithm for sampling from the marginal posterior of a general integrable mixture that makes use of rejection-free sampling from the prior over component assignments to achieve excellent mixing times in typical applications, outperforming standard Gibbs sampling, in some cases by a wide margin. We demonstrate the approach with a selection of applications to Gaussian, Poisson, and categorical models.