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Multi-view data have been routinely collected in various fields of scienceand engineering. A general problem is to study the predictive associationbetween multivariate responses and multi-view predictor sets, all of which canbe of high dimensionality. It is likely that only a few views are relevant toprediction, and the predictors within each relevant view contribute to theprediction collectively rather than sparsely. We cast this new problem underthe familiar multivariate regression framework and propose an integrativereduced-rank regression (iRRR), where each view has its own low-rankcoefficient matrix. As such, latent features are extracted from each view in asupervised fashion. For model estimation, we develop a convex composite nuclearnorm penalization approach, which admits an efficient algorithm via alternatingdirection method of multipliers. Extensions to non-Gaussian and incomplete dataare discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRRunder a restricted eigenvalue condition. Our results recover oracle bounds ofseveral special cases of iRRR including Lasso, group Lasso and nuclear normpenalized regression. Therefore, iRRR seamlessly bridges group-sparse andlow-rank methods and can achieve substantially faster convergence rate underrealistic settings of multi-view learning. Simulation studies and anapplication in the Longitudinal Studies of Aging further showcase the efficacyof the proposed methods.

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