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

Sai Li, T. Tony Cai and Hongzhe Li

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 1, 149-173

Abstract: 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.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/rssb.12479

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:84:y:2022:i:1:p:149-173

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().