Robust angle-based transfer learning in high dimensions

Transfer learning aims to improve the performance of a target model by leveraging data from related source populations. It is known to be especially helpful in cases with insufficient target data. In this paper, we study the problem of how to train a high-dimensional ridge regression model with limited target data and existing models trained in heterogeneous source populations. We consider a practical setting where only the source model parameters are accessible, instead of the individual-level source data. Under the setting with only one source model, we propose a novel flexible angle-based transfer learning (angleTL) method, which leverages the concordance between the source and the target model parameters. We show that angleTL unifies several benchmark methods by construction, including the target-only model trained using target data alone, the source model trained using the source data, and the distance-based transfer learning method that incorporates the source model to the target training by penalizing the difference between the target and source model parameters measured by the $L_2$ norm. We also provide algorithms to effectively incorporate multiple source models accounting for the fact that some source models may be more helpful than others. Our high-dimensional asymptotic analysis provides interpretations and insights regarding when a source model can be helpful to the target model, and demonstrates the superiority of angleTL over other benchmark methods. We perform extensive simulation studies to validate our theoretical conclusions and show the feasibility of applying angleTL to transfer existing genetic risk prediction models across multiple biobanks.