# Model Selection for Mixture Models - Perspectives and Strategies

arXiv: https://arxiv.org/abs/1812.09885 · HTML: https://mlsanity.com/paper/1812.09885/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2018.

## Built on by (most cited first, 5 of 5)

- [Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?](https://mlsanity.com/paper/2207.14717/) (2022)
- [Learn2Extend: Extending sequences by retaining their statistical properties with mixture models](https://mlsanity.com/paper/2312.01507/) (2023)
- [VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data](https://mlsanity.com/paper/2406.16227/) (2024)
- [Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review](https://mlsanity.com/paper/2505.07911/) (2025)
- [Effective regions and kernels in continuous sparse regularisation, with application to sketched mixtures](https://mlsanity.com/paper/2507.08444/) (2025)

## Abstract (arXiv)

Determining the number G of components in a finite mixture distribution is an important and difficult inference issue. This is a most important question, because statistical inference about the resulting model is highly sensitive to the value of G. Selecting an erroneous value of G may produce a poor density estimate. This is also a most difficult question from a theoretical perspective as it relates to unidentifiability issues of the mixture model. This is further a most relevant question from a practical viewpoint since the meaning of the number of components G is strongly related to the modelling purpose of a mixture distribution. We distinguish in this chapter between selecting G as a density estimation problem in Section 2 and selecting G in a model-based clustering framework in Section 3. Both sections discuss frequentist as well as Bayesian approaches. We present here some of the Bayesian solutions to the different interpretations of picking the "right" number of components in a mixture, before concluding on the ill-posed nature of the question.