Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression
Year: 2026
Type: preprint
Abstract: This paper studies transfer learning for high-dimensional quantile regression with limited target samples and heterogeneous source domains. We propose a sample-level transfer learning method (SL-TL) that combines sample selection and importance weighting. Unlike existing source-level approaches that include or exclude entire source domains, SL-TL identifies transferable samples within each source domain and incorporates them through adaptive importance weights. The proposed weights rely only on one-dimensional densities associated with the quantile loss, avoiding the estimation of high-dimensional density ratios. We establish error bounds for SL-TL estimators and characterize the effective sample size contributed by source domains. In the oracle setting, we show that SL-TL achieves faster $\ell_2$-convergence rates than existing competitors under the considered regimes. For the unknown setting, we develop an implementable algorithm based on sample splitting and cross-fitting procedures. Extensive simulations and a real data analysis demonstrate the finite-sample performance and robustness of SL-TL.
Source: arXiv (Cornell University)
Authors: Xing, Xiangyu, Wang, Yingxuan, Xu, Wangli
Institution: Renmin University of China
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Renmin University of China
OpenAlex ID: W7220931976