Robust feature selection via l2,1-norm in finite mixture of regression

Finite mixture of Gaussian regression (FMR) is a widely-used modeling technique in supervised learning problems. In cases where the number of features is large, feature selection is desirable to enhance model interpretability and to avoid overfitting. In this paper, we propose a robust feature selection method via l(2,1)-norm penalized maximum likelihood estimation (MLE) in FMR, with extension to sparse l(2,1) penalty by combining l(1)-norm with l(2,1)-norm for increasing flexibility. To solve the non-convex and non-smooth problem of (sparse) penalized MLE in FMR, we develop an new EM-based algorithm for numerical optimization, with combination of block coordinate descent and majorizing-mimmization scheme in M-step. We finally apply our method in six simulations and one real dataset to demonstrate its superior performance. (c) 2018 Elsevier B.V. All rights reserved.