  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.
