Transfer learning for high-dimensional linear regression: Prediction, estimation and minimax optimality

• 成果类型: Article
• 署名作者: Li, Sai; Cai, T. Tony; Li, Hongzhe
• 署名单位: University of Pennsylvania; University of Pennsylvania
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12479
• 发表日期: 2022
• 页码: 149-173
• 关键词: VARIABLE SELECTION; Optimal Rates; Lasso

摘要

This paper considers estimation and prediction of a high-dimensional linear regression in the setting of transfer learning where, in addition to observations from the target model, auxiliary samples from different but possibly related regression models are available. When the set of informative auxiliary studies is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. When the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and show its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating data from multiple different tissues as auxiliary samples.