Integrative Multi-View Reduced-Rank Regression: Bridging Group-Sparse and Low-Rank Models
This work addresses predictive modeling for multi-view data in fields like science and engineering, offering a novel integration of existing methods but is incremental in combining group-sparse and low-rank approaches.
The paper tackles the problem of predicting multivariate responses from high-dimensional multi-view data, where only a few views are relevant and predictors contribute collectively, by proposing an integrative reduced-rank regression (iRRR) method that bridges group-sparse and low-rank models, achieving faster convergence rates in simulations and an aging study application.
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.