Robust weighted transfer learning with linear constraints under linear regressive model

Transfer learning is a method aimed at enhancing the estimation and prediction accuracy of a target model by transferring the source data when there is limited data available for the target domain. However, existing transfer learning approaches often overlook the heterogeneity and heavy-tailed nature of high-dimensional data. Therefore, we consider Huber regression, which is robust to thick-tailed distributed data and outliers. In this article, based on the residual importance-based transfer learning, the constraints of a priori information are added to carry out the research of robust transfer learning, the coefficients of the target model are estimated by using Huber regression, and the effectiveness of the method is proved by simulation experiments and real cases.