A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting
This work addresses model selection and parameter estimation for mixture models in a family setting, but it is incremental as it proposes an alternative to the established EM-BIC rubric.
The authors tackled the problem of parameter estimation and model selection in Gaussian mixture models by developing a variational Bayes approach with the deviance information criterion, which they compared to the standard EM-BIC method using real and simulated data, showing competitive performance.
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.