Parallel integrative learning for large-scale multi-response regression with incomplete outcomes

TL;DR

This paper introduces PEER, a scalable parallel method for large-scale multi-response regression with incomplete data, achieving accurate estimation, variable selection, and computational efficiency in high-dimensional settings.

Contribution

The paper proposes PEER, a novel parallelizable approach for multi-response regression with incomplete outcomes, handling high-dimensional responses and predictors efficiently.

Findings

PEER outperforms existing methods in accuracy and speed.

PEER maintains consistency in estimation and variable selection.

Simulation studies validate PEER's effectiveness in large-scale scenarios.

Abstract

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.