# Clustering consistency with Dirichlet process mixtures

arXiv: https://arxiv.org/abs/2205.12924 · HTML: https://mlsanity.com/paper/2205.12924/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 4 of 4)

- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Inconsistency of Pitman-Yor process mixtures for the number of components](https://mlsanity.com/paper/1309.0024/) (2013)
- [Finite mixture models do not reliably learn the number of components](https://mlsanity.com/paper/2007.04470/) (2020)
- [Posterior Distribution for the Number of Clusters in Dirichlet Process Mixture Models](https://mlsanity.com/paper/1905.09959/) (2019)

## Built on by (most cited first, 6 of 6)

- [Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?](https://mlsanity.com/paper/2207.14717/) (2022)
- [Fair Clustering via Hierarchical Fair-Dirichlet Process](https://mlsanity.com/paper/2305.17557/) (2023)
- [Scalable Posterior Uncertainty for Flexible Density-Based Clustering](https://mlsanity.com/paper/2603.03188/) (2026)
- [Entropy regularization in probabilistic clustering](https://mlsanity.com/paper/2307.10065/) (2023)
- [Spectral gap of Metropolis-within-Gibbs under log-concavity](https://mlsanity.com/paper/2509.26175/) (2025)
- [Nested Atoms Model with Application to Clustering Big Population-Scale Single-Cell Data](https://mlsanity.com/paper/2604.11731/) (2026)

## Abstract (arXiv)

Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration parameter of the underlying Dirichlet process. Previous findings in the literature suggest that Dirichlet process mixtures are typically not consistent for the number of clusters if the concentration parameter is held fixed and data come from a finite mixture. Here we show that consistency for the number of clusters can be achieved if the concentration parameter is adapted in a fully Bayesian way, as commonly done in practice. Our results are derived for data coming from a class of finite mixtures, with mild assumptions on the prior for the concentration parameter and for a variety of choices of likelihood kernels for the mixture.