A sequential stepwise screening procedure for sparse recovery in high-dimensional multiresponse models with complex group structures

Multiresponse data with complex group structures in both responses and predictors arises in many fields, yet, due to the difficulty in identifying complex group structures, only a few methods have been studied on this problem. We propose a novel algorithm called sequential stepwise screening procedure (SeSS) for feature selection in high-dimensional multiresponse models with complex group structures. This algorithm encourages the grouping effect, where responses and predictors come from different groups, further, each response group is allowed to relate to multiple predictor groups. To obtain a correct model under the complex group structures, the proposed procedure first chooses the nonzero block and the nonzero row by the canonical correlation measure (CC) and then selects the nonzero entries by the extended Bayesian Information Criterion (EBIC). We show that this method is accurate in extremely sparse models and computationally attractive. The theoretical property of SeSS is established. We conduct simulation studies and consider a real example to compare its performances with existing methods.