期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 157, 期 -, 页码 14-28出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2017.02.007
关键词
Bayesian; Low rank; Posterior consistency; Rank reduction; Sparsity
资金
- U.S. National Institutes of Health [U01-HL114494]
- U.S. National Science Foundation [DMS-1613295]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1613295] Funding Source: National Science Foundation
Many modern statistical problems can be cast in the framework of multivariate regression, where the main task is to make statistical inference for a possibly sparse and low-rank coefficient matrix. The low-rank structure in the coefficient matrix is of intrinsic multivariate nature, which, when combined with sparsity, can further lift dimension reduction, conduct variable selection, and facilitate model interpretation. Using a Bayesian approach, we develop a unified sparse and low-rank multivariate regression method to both estimate the coefficient matrix and obtain its credible region for making inference. The newly developed sparse and low-rank prior for the coefficient matrix enables rank reduction, predictor selection and response selection simultaneously. We utilize the marginal likelihood to determine the regularization hyperparameter, so our method maximizes its posterior probability given the data. For theoretical aspect, the posterior consistency is established to discuss an asymptotic behavior of the proposed method. The efficacy of the proposed approach is demonstrated via simulation studies and a real application on yeast cell cycle data. (C) 2017 Elsevier Inc. All rights reserved.
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