Robust transfer learning for high-dimensional quantile regression model with linear constraints

Transfer learning has emerged as a crucial technique for leveraging source domain information to enhance the performance of target tasks. However, existing transfer learning methods often overlook the heterogeneity and heavy-tailed nature of high-dimensional data, which can potentially undermine the final performance. This study aims to address the problem of high-dimensional quantile regression within the context of transfer learning and investigates the impact of incorporating linear constraints. In the case of known transferable sources, a two-step transfer learning algorithm is proposed in this study. To mitigate the negative effects of including non-informative sources, a transferable source detection algorithm based on cross-validation is introduced. The effectiveness of the proposed methods and the significant performance improvement achieved by incorporating linear constraints are demonstrated through numerical simulations and empirical analysis using used car transaction data.