Transfer Learning for High-dimensional Quantile Regression with Statistical Guarantee

Published: 17 Feb 2024, Last Modified: 17 Feb 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: The task of transfer learning is to improve estimation/inference of a target model by migrating data from closely related source populations. In this article, we propose transfer learning algorithms for high-dimensional Quantile Regression (QR) models with the technique of convolution-type smoothing. Given the transferable source populations, we derive $\ell_1/\ell_2$-estimation error bounds for the estimators of the target regression coefficients under mild conditions. Theoretical analysis shows that the upper bounds are improved over those of the classical penalized QR estimator with only the target data, as long as the target and the sources are sufficiently similar to each other. When the set of informative sources is unknown, a transferable source detection algorithm is proposed to detect informative sources from all available sources. Thorough simulation studies justify our theoretical analysis.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: * Corrected some typos. * Added acknowledgment section. * Adjusted the DPI of some figures.
Assigned Action Editor: ~Bryon_Aragam1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1354