# Model Selection for Gaussian Mixture Models

arXiv: https://arxiv.org/abs/1301.3558 · HTML: https://mlsanity.com/paper/1301.3558/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

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

- [Adversarially robust clustering with optimality guarantees](https://mlsanity.com/paper/2306.09977/) (2023)
- [Robust Model Selection and Nearly-Proper Learning for GMMs](https://mlsanity.com/paper/2106.02774/) (2021)
- [RCC-GAN: Regularized Compound Conditional GAN for Large-Scale Tabular Data Synthesis](https://mlsanity.com/paper/2205.11693/) (2022)
- [The Parametric Stability of Well-separated Spherical Gaussian Mixtures](https://mlsanity.com/paper/2302.00242/) (2023)
- [Fast estimation of Gaussian mixture components via centering and singular value thresholding](https://mlsanity.com/paper/2604.19091/) (2026)
- [Coupled Usage-Sense Processes: Temporal and Attributable Lexical Semantic Change](https://mlsanity.com/paper/2609.30974/) (2026)

## Abstract (arXiv)

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models. The proposed method is shown to be statistically consistent in determining of the number of components. A modified EM algorithm is developed to simultaneously select the number of components and to estimate the mixing weights, i.e. the mixing probabilities, and unknown parameters of Gaussian distributions. Simulations and a real data analysis are presented to illustrate the performance of the proposed method.