Feature Selection in High-Dimensional Models via EBIC with Energy Distance Correlation.

In this paper, the LASSO method with extended Bayesian information criteria (EBIC) for feature selection in high-dimensional models is studied. We propose the use of the energy distance correlation in place of the ordinary correlation coefficient to measure the dependence of two variables. The energy distance correlation detects linear and non-linear association between two variables, unlike the ordinary correlation coefficient, which detects only linear association. EBIC is adopted as the stopping criterion. It is shown that the new method is more powerful than Luo and Chen's method for feature selection. This is demonstrated by simulation studies and illustrated by a real-life example. It is also proved that the new algorithm is selection-consistent.