Reduced rank stochastic regression with a sparse singular value decomposition

• 成果类型: Article
• 署名作者: Chen, Kun; Chan, Kung-Sik; Stenseth, Nils Chr.
• 署名单位: University of Iowa; Kansas State University; University of Oslo
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2011.01002.x
• 发表日期: 2012
• 页码: 203-221
• 关键词: VARIABLE SELECTION; regularization; dimension; Lasso

摘要

. For a reduced rank multivariate stochastic regression model of rank r*, the regression coefficient matrix can be expressed as a sum of r* unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank regression approach for solving this problem. Computation algorithms and regularization parameter selection methods are developed, and the properties of the new method are explored both theoretically and by simulation. In particular, the regularization method proposed is shown to be selection consistent and asymptotically normal and to enjoy the oracle property. We apply the proposed model to perform biclustering analysis with microarray gene expression data.