Transfer Learning for High-dimensional Quantile Regression with Distribution Shift

作     者：Bai, Ruiqi Zhang, Yijiao Yang, Hanbo Zhu, Zhongyi 

作者机构：Department of Statistics and Data Science Fudan University China School of the Gifted Young University of Science and Technology of China China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Contrastive Learning 

摘      要：Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional regression setting, existing transfer approaches mainly focus on the parameter shift. In this paper, we focus on the high-dimensional quantile regression with knowledge transfer under three types of distribution shift: parameter shift, covariate shift, and residual shift. We propose a novel transferable set and a new transfer framework to address the above three discrepancies. Non-asymptotic estimation error bounds and source detection consistency are established to validate the availability and superiority of our method in the presence of distribution shift. Additionally, an orthogonal debiased approach is proposed for statistical inference with knowledge transfer, leading to sharper asymptotic results. Extensive simulation results as well as real data applications further demonstrate the effectiveness of our proposed procedure. Copyright © 2024, The Authors. All rights reserved.