Reduced rank regression via adaptive nuclear norm penalization

• 成果类型: Article
• 署名作者: Chen, Kun; Dong, Hongbo; Chan, Kung-Sik
• 署名单位: University of Connecticut; University of Wisconsin System; University of Wisconsin Madison; University of Iowa
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast036
• 发表日期: 2013
• 页码: 901920
• 关键词: dimension reduction; variable selection; matrix; estimators; Lasso; likelihood; algorithm; number

摘要

We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally nonconvex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed nonconvex penalized regression method has a global optimal solution obtained from an adaptively soft-thresholded singular value decomposition. The method is computationally efficient, and the resulting solution path is continuous. The rank consistency of and prediction/estimation performance bounds for the estimator are established for a high-dimensional asymptotic regime. Simulation studies and an application in genetics demonstrate its efficacy.