# Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?

arXiv: https://arxiv.org/abs/2207.14717 · HTML: https://mlsanity.com/paper/2207.14717/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 78 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 19 of 19)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/1810.05691/) (2018)
- [A Bayesian information criterion for singular models](https://mlsanity.com/paper/1309.0911/) (2013)
- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [Search Algorithms and Loss Functions for Bayesian Clustering](https://mlsanity.com/paper/2105.04451/) (2021)
- [Bayesian Consensus Clustering](https://mlsanity.com/paper/1302.7280/) (2013)
- [Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure](https://mlsanity.com/paper/2005.11641/) (2020)
- [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)
- [Clustering consistency with Dirichlet process mixtures](https://mlsanity.com/paper/2205.12924/) (2022)
- [Probabilistic community detection with unknown number of communities](https://mlsanity.com/paper/1602.08062/) (2016)
- [Optimal Bayesian estimators for latent variable cluster models](https://mlsanity.com/paper/1607.02325/) (2016)
- [Scalable Bayesian Nonparametric Clustering and Classification](https://mlsanity.com/paper/1806.02670/) (2018)
- [Model Selection for Mixture Models - Perspectives and Strategies](https://mlsanity.com/paper/1812.09885/) (2018)
- [Extended Stochastic Block Models with Application to Criminal Networks](https://mlsanity.com/paper/2007.08569/) (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, 1 of 1)

- [VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data](https://mlsanity.com/paper/2406.16227/) (2024)

## Abstract (arXiv)

We consider the Bayesian mixture of finite mixtures (MFMs) and Dirichlet process mixture (DPM) models for clustering. Recent asymptotic theory has established that DPMs overestimate the number of clusters for large samples and that estimators from both classes of models are inconsistent for the number of clusters under misspecification, but the implications for finite sample analyses are unclear. The final reported estimate after fitting these models is often a single representative clustering obtained using an MCMC summarisation technique, but it is unknown how well such a summary estimates the number of clusters. Here we investigate these practical considerations through simulations and an application to gene expression data, and find that (i) DPMs overestimate the number of clusters even in finite samples, but only to a limited degree that may be correctable using appropriate summaries, and (ii) misspecification can lead to considerable overestimation of the number of clusters in both DPMs and MFMs, but results are nevertheless often still interpretable. We provide recommendations on MCMC summarisation and suggest that although the more appealing asymptotic properties of MFMs provide strong motivation to prefer them, results obtained using MFMs and DPMs are often very similar in practice.