In this paper, we consider the regularized multi-response regression problem where there exists some structural relation within the responses and also between the covariates and a set of modifying variables. To handle this problem, we propose MADMMplasso, a novel regularized regression method. This method is able to find covariates and their corresponding interactions, with some joint association with multiple related responses. We allow the interaction term between covariate and modifying variable to be included in a (weak) asymmetrical hierarchical manner by first considering whether the corresponding covariate main term is in the model. For parameter estimation, we develop an ADMM algorithm that allows us to implement the overlapping groups in a simple way. The results from the simulations and analysis of a pharmacogenomic screen data set show that the proposed method has an advantage in handling correlated responses and interaction effects, both with respect to prediction and variable selection performance.

翻译：本文研究了正则化多响应回归问题，其中响应变量之间存在某种结构关系，协变量与一组修正变量之间也存在关联。针对这一问题，我们提出了一种新颖的正则化回归方法——MADMMplasso。该方法能够识别与多个相关响应具有联合关联的协变量及其对应的交互效应。我们允许协变量与修正变量之间的交互项以（弱）非对称层次方式纳入模型，即首先考虑相应协变量主效应项是否存在于模型中。在参数估计方面，我们开发了一种ADMM算法，能够以简单的方式实现重叠分组。模拟实验和药物基因组学筛查数据集的分析结果表明，所提方法在处理相关响应和交互效应方面具有优势，在预测性能和变量选择性能上均表现优异。