Journal article
Reduced rank regression via adaptive nuclear norm penalization
Biometrika, Vol.100(4), pp.901-920
12/04/2013
DOI: 10.1093/biomet/ast036
PMCID: PMC4101086
PMID: 25045172
Abstract
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 non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex 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.
Details
- Title: Subtitle
- Reduced rank regression via adaptive nuclear norm penalization
- Creators
- Kun Chen - Department of Statistics, University of Connecticut, 215 Glenbrook Road, Storrs, Connecticut 06269, U.S.AHongbo Dong - Wisconsin Institutes for Discovery, University of Wisconsin, 330 N. Orchard St., Madison, Wisconsin 53715, U.S.AKung-Sik Chan - Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A
- Resource Type
- Journal article
- Publication Details
- Biometrika, Vol.100(4), pp.901-920
- DOI
- 10.1093/biomet/ast036
- PMID
- 25045172
- PMCID
- PMC4101086
- NLM abbreviation
- Biometrika
- ISSN
- 0006-3444
- eISSN
- 1464-3510
- Language
- English
- Date published
- 12/04/2013
- Academic Unit
- Statistics and Actuarial Science; Radiology
- Record Identifier
- 9983985880102771
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