Multi-task learning is increasingly used to investigate the association structure between multiple responses and a single set of predictor variables in many applications. In the era of big data, the coexistence of incomplete outcomes, large number of responses, and high dimensionality in predictors poses unprecedented challenges in estimation, prediction and computation. In this paper, we propose a scalable and computationally efficient procedure, called PEER, for large-scale multi-response regression with incomplete outcomes, where both the numbers of responses and predictors can be high-dimensional. Motivated by sparse factor regression, we convert the multi-response regression into a set of univariate-response regressions, which can be efficiently implemented in parallel. Under some mild regularity conditions, we show that PEER enjoys nice sampling properties including consistency in estimation, prediction, and variable selection. Extensive simulation studies show that our proposal compares favorably with several existing methods in estimation accuracy, variable selection, and computation efficiency.

在许多应用程序中，越来越多地使用多任务学习来研究多个响应和一组预测变量之间的关联结构。在大数据时代，不完整的结果，大量的响应以及预测变量的高共存性在估计，预测和计算方面提出了前所未有的挑战。在本文中，我们提出了一种可扩展的，计算效率高的过程，称为PEER，用于不完整结果的大规模多响应回归，其中响应和预测变量的数量都可以是高维的。出于稀疏因子回归的考虑，我们将多响应回归转换为一组单变量响应回归，可以有效地并行执行。在一些温和的规律性条件下，我们表明，PEER具有良好的采样属性，包括估计，预测和变量选择的一致性。大量的仿真研究表明，我们的建议在估计精度，变量选择和计算效率方面与几种现有方法相比具有优势。