On cross-validation for sparse reduced rank regression

• 成果类型: Article
• 署名作者: She, Yiyuan; Hoang Tran
• 署名单位: State University System of Florida; Florida State University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12295
• 发表日期: 2019
• 页码: 145-161
• 关键词: simultaneous dimension reduction; Principal Component Analysis; model selection; number; Lasso

摘要

In high dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received much attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. Our in-sample error studies in jointly sparse and rank deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. By use of an identity, we propose a novel scale-free calibration to help cross-validation to achieve the minimax optimal error rate non-asymptotically. Experiments support the efficacy of the methods proposed.