# A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting

arXiv: https://arxiv.org/abs/1306.5368 · HTML: https://mlsanity.com/paper/1306.5368/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2013.

## Built on by (most cited first, 1 of 1)

- [Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Data](https://mlsanity.com/paper/2311.07762/) (2023)

## Abstract (arXiv)

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decomposed and a number of constraints are imposed. Within the family setting, model selection involves choosing the member of the family, i.e., the appropriate covariance structure, in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for model selection, and the expectation-maximization (EM) algorithm is usually used for parameter estimation. In fact, this EM-BIC rubric has virtually monopolized the literature on families of mixture models. Deviating from this rubric, variational Bayes approximations are developed for parameter estimation and the deviance information criterion for model selection. The variational Bayes approach provides an alternate framework for parameter estimation by constructing a tight lower bound on the complex marginal likelihood and maximizing this lower bound by minimizing the associated Kullback-Leibler divergence. This approach is taken on the most commonly used family of Gaussian mixture models, and real and simulated data are used to compare the new approach to the EM-BIC rubric.