Transfer Learning for High Dimensional Robust Regression

Abstract: Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic variance or inhomogeneous covariate effects. To solve this problem, this paper proposes a robust transfer learning based on the Huber regression, specifically designed for scenarios where the transferable source data set is known. This method effectively mitigates the impact of data heteroscedasticity, leading to improvements in estimation and prediction accuracy. Moreover, when the transferable source data set is unknown, the paper introduces an efficient detection algorithm to identify informative sources. The effectiveness of the proposed method is proved through numerical simulation and empirical analysis using superconductor data.