Adaptive Sparse Reduced-Rank Regression

• Activity Number: 275
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Tingni Sun*+ and Zongming Ma
• Companies: University of Pennsylvania and Wharton School
• Keywords: Multivariate regression ; High-dimensional statistics ; Sparsity ; Low rankness ; Minimax rates ; Schatten norm

Abstract

This talk concerns the reduced-rank regression model in the high-dimensional setting, which contains multivariate or even high-dimensional response variables together with a large number of predictors, while the sample size can be much smaller. We proposed a new estimation scheme for coefficient matrix, where both dimension reduction and variable selection are taken into account. We derived the error bounds with respect to a class of squared Schatten norm loss functions for the proposed estimator and showed that it achieves near optimal rates adaptively. The practical competitiveness of the estimator is further demonstrated through numerical studies.