Regularization in Finite Mixture of Regression Models with Diverging Number of Parameters

Abstract

Feature (variable) selection has become a fundamentally important problem in recent statistical literature. Sometimes, in applications, many variables are introduced to reduce possible modeling biases, but the number of variables a model can accommodate is often limited by the amount of data available. In other words, the number of variables considered depends on the sample size, which reflects the estimability of the parametric model. In this article, we consider the problem of feature selection in finite mixture of regression models when the number of parameters in the model can increase with the sample size. We propose a penalized likelihood approach for feature selection in these models. Under certain regularity conditions, our approach leads to consistent variable selection. We carry out extensive simulation studies to evaluate the performance of the proposed approach under controlled settings. We also applied the proposed method to two real data. The first is on telemonitoring of Parkinson's disease (PD), where the problem concerns whether dysphonic features extracted from the patients' speech signals recorded at home can be used as surrogates to study PD severity and progression. The second is on breast cancer prognosis, in which one is interested in assessing whether cell nuclear features may offer prognostic values on long-term survival of breast cancer patients. Our analysis in each of the application revealed a mixture structure in the study population and uncovered a unique relationship between the features and the response variable in each of the mixture component.