Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression
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 ℓ2-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.
Related
- Joint-Sparse Transfer Learning for High-Dimensional Multi-Output Regression
- Global Inference for High Dimensional Quantile Regression with Heterogeneity
- Transfer Learning with Heterogeneous Feature Spaces in Linear Regression
- Augmented transfer regression learning for completely missing covariates
- Minimax-optimal Scaling Laws in Ridge Regression via Transfer Learning
BibTeX
@misc{xing2026beyond,
title = {{Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression}},
author = {Xiangyu Xing and Yingxuan Wang and Wangli Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09722},
eprint = {2610.09722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09722},
}
RIS
TY - UNPB
TI - Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression
AU - Xiangyu Xing
AU - Yingxuan Wang
AU - Wangli Xu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09722
UR - https://arxiv.org/abs/2610.09722
AB - 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 ℓ_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.
ER -