Transfer learning with high dimensional composite quantile regression

Transfer learning has gained wide popularity due to its ability to enhance the performance of target tasks by utilizing external information sources. Despite this, current transfer learning methods often struggle to consistently and effectively handle heterogeneous and/or heavy tail data. To address this issue, we propose a robust transfer learning method based on the composite quantile regression model that can adapt to a variety of data types and integrate multiple quantile information. Additionally, this method can handle situations where the error term variance is infinite. A challenging scenario in transfer learning is that the transferable data set is unknown, so we design two detection algorithms to correctly identify valid transferable data sets. Through numerical simulations and empirical analysis, we verify the good performance of the above algorithms based on the high-dimensional composite quantile regression model.