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Abstract:
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We introduce an integrated reduced-rank framework for multivariate regression. Predictors are multi-view data, which naturally form different groups. Each predictor group has its unique low-rank coefficient matrix. The framework flexibly captures the relationship between multivariate responses and predictors, and subsumes many existing methods such as reduced rank regression and group lasso as special cases. We develop an efficient alternating direction method of multipliers (ADMM) algorithm for model fitting, and exploit a majorization approach to deal with binary responses or missing values in responses. We demonstrate the efficacy of the proposed methods with simulation studies and a real application to the Longitudinal Study of Aging. Theoretical properties are also studied.
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