Robust transfer learning for high-dimensional regression with linear constraints

Transfer learning is a method to improve the estimation and prediction accuracy of the target model by transferring the source data when the available data of the target data is relatively few. However, existing transfer learning methods tend to ignore the heterogeneity and heavy-tailedness of high-dimensional data. So we consider the Huber regression, which is robust to thick-tailed distributed data and outliers. Based on the high-dimensional model, this paper adds the constraint conditions of prior information, carries out the research of robust transfer learning and uses Huber regression to estimate the coefficients of the target model. In this paper, we design corresponding transfer learning algorithms for known and unknown transferable sources, and prove the effectiveness of this method through simulation experiments and actual cases.