Integrative Multi-View Reduced-Rank Regression: Bridging Group-Sparse and Low-Rank Models

TL;DR

This paper introduces an integrative reduced-rank regression method for multi-view high-dimensional data, effectively combining group-sparse and low-rank models to improve prediction and interpretability.

Contribution

It proposes a novel convex nuclear norm penalization approach for multi-view regression, bridging existing sparse and low-rank methods with theoretical guarantees.

Findings

Achieves faster convergence rates in multi-view learning scenarios.

Recovers oracle bounds of Lasso, group Lasso, and nuclear norm methods.

Demonstrates effectiveness through simulations and real data application.

Abstract

Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced-rank regression (iRRR), where each view has its own low-rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non-Gaussian and incomplete data are discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group-sparse and low-rank methods and can achieve substantially faster convergence rate under realistic settings of multi-view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods.