# A Two-round Variant of EM for Gaussian Mixtures

arXiv: https://arxiv.org/abs/1301.3850 · HTML: https://mlsanity.com/paper/1301.3850/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

## Built on by (most cited first, 11 of 11)

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- [Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Models](https://mlsanity.com/paper/2407.00490/) (2024)
- [Lower Bounds on the Total Variation Distance Between Mixtures of Two Gaussians](https://mlsanity.com/paper/2109.01064/) (2021)
- [On unsupervised projections and second order signals](https://mlsanity.com/paper/2204.05139/) (2022)
- [Mixture-Models: a one-stop Python Library for Model-based Clustering using various Mixture Models](https://mlsanity.com/paper/2402.10229/) (2024)
- [Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modeling](https://mlsanity.com/paper/2507.20459/) (2025)
- [Semidefinite programming on population clustering: a global analysis](https://mlsanity.com/paper/2301.00344/) (2023)
- [Optimal Transport for Kernel Gaussian Mixture Models](https://mlsanity.com/paper/2310.18586/) (2023)
- [Learning Overspecified Gaussian Mixtures Exponentially Fast with the EM Algorithm](https://mlsanity.com/paper/2506.11850/) (2025)
- [Overspecified Mixture Discriminant Analysis: Exponential Convergence, Statistical Guarantees, and Remote Sensing Applications](https://mlsanity.com/paper/2510.27056/) (2025)

## Abstract (arXiv)

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.