Parametric and semiparametric reduced-rank regression with flexible sparsity

JOURNAL OF MULTIVARIATE ANALYSIS

卷:136

Article

Lian, Heng^1,3  Feng, Sanying²  Zhao, Kaifeng¹ 

[1] Nanyang Technol Univ, Div Math Sci, Singapore 637371, Singapore

[2] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[3] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

关键词: Additive models;    Oracle inequality;    Reduced-rank regression;    Sparse group lasso;   

DOI  :  10.1016/j.jmva.2015.01.013

来源: Elsevier

【 摘 要 】

We consider joint rank and variable selection in multivariate regression. Previously proposed joint rank and variable selection approaches assume that different responses are related to the same set of variables, which suggests using a group penalty on the rows of the coefficient matrix. However, this assumption may not hold in practice and motivates the usual lasso (l(1)) penalty on the coefficient matrix. We propose to use the gradient-proximal algorithm to solve this problem, which is a recent development in optimization. We also present some theoretical results for the proposed estimator with the l(1) penalty. We then consider several extensions including adaptive lasso penalty, sparse group penalty, and additive models. The proposed methodology thus offers a much more complete set of tools in high-dimensional multivariate regression. Finally, we present numerical illustrations based on simulated and real data sets. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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