Feature selection in finite mixture of sparse normal linear models in high-dimensional feature space.

Rapid advancement in modern technology has allowed scientists to collect data of unprecedented size and complexity. This is particularly the case in genomics applications. One type of statistical problem in such applications is concerned with modeling an output variable as a function of a small subset of a large number of features based on relatively small sample sizes, which may even be coming from multiple subpopulations. As such, selecting the correct predictive features (variables) for each subpopulation is the key. To address this issue, we consider the problem of feature selection in finite mixture of sparse normal linear (FMSL) models in large feature spaces. We propose a 2-stage procedure to overcome computational difficulties and large false discovery rates caused by the large model space. First, to deal with the curse of dimensionality, a likelihood-based boosting is designed to effectively reduce the number of candidate features. This is the key thrust of our new method. The greatly reduced set of features is then subjected to a sparsity inducing procedure via a penalized likelihood method. A novel scheme is also proposed for the difficult problem of finding good starting points for the expectation-maximization estimation of mixture parameters. We use an extended Bayesian information criterion to determine the final FMSL model. Simulation results indicate that the procedure is successful in selecting the significant features without including a large number of insignificant ones. A real data example on gene transcription regulation is also presented.