Transfer Learning for High-Dimensional Quantile Regression with Statistical Guarantee

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.