Feature Selection by Canonical Correlation Search in High-Dimensional Multiresponse Models With Complex Group Structures

High-dimensional multiresponse models with complex group structures in both the response variables and the covariates arise from current researches in important fields such as genetics and medicine. However, no enough research has been done on such models. One of a few researches, if not the only one, is the article by Li, Nan, and Zhu where the sparse group Lasso approach is extended to such models. In this article, we propose a novel approach named the sequential canonical correlation search (SCCS) procedure. In the SCCS procedure, the nonzero group by group blocks of regression coefficients are searched stepwise using a canonical correlation measure. Each step of the procedure consists of a block selection and a sparsity identification. The model selection criterion, EBIC, is used as the stopping rule of the procedure. We establish the selection consistency of the SCCS procedure and conduct simulation studies for the comparison of existing methods. The SCCS procedure has two advantages over the sparse grouped Lasso method: (i) it is more accurate in the identification of nonzero coefficient blocks and their nonzero entries, and (ii) its implementation is not limited by the dimensionality of the models and requires much less computation. A real example in genetic studies is also considered. Supplementary materials for this article are available online.