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.

翻译：在许多领域,由于难以确定复杂的组群结构,因此对该问题只研究了若干方法。我们建议了一种新型算法,称为顺序分步筛选程序(SeSS),用于在具有复杂组群结构的高维多应对模型中选择特征。这种算法鼓励组合效应,因为反应和预测器来自不同组群,而且允许每个响应组与多个预测组群有关。为了在复杂的组群结构下获得正确的模型,拟议的程序首先选择非零块和非零行,然后选择延伸的贝叶西亚信息标准(EBIC)的非零条目。我们表明,这种方法在极为稀少的模型中是准确的,在计算上具有吸引力。SeSS的理论属性已经建立。我们进行模拟研究,并且考虑将它的业绩与现有方法进行比较的实际例子。