Transfer learning aims to improve the performance of a target model by leveraging data from related source populations, which 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 using limited target data and existing regression models trained in heterogeneous source populations. We consider a practical setting where only the parameter estimates of the fitted source models 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 fitted on source data, and distance-based transfer learning method that incorporates the source parameter estimates and the target data under a distance-based similarity constraint. 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.

翻译：迁移学习旨在通过利用来自相关源群体的数据来提升目标模型的性能，这在目标数据不足的情况下尤为有效。本文研究了如何利用有限的目标数据及已在异构源群体中训练的现有回归模型，训练高维岭回归模型的问题。我们考虑一个实际场景：仅能获取源模型拟合后的参数估计值，而非个体层面的源数据。在仅有一个源模型的设定下，我们提出一种新型的灵活角度迁移学习方法（angleTL），该方法利用了源模型与目标模型参数之间的一致性。我们证明，angleTL在构造上统一了多种基准方法，包括仅使用目标数据训练的目标单模型、基于源数据拟合的源模型，以及在距离相似性约束下融合源参数估计值与目标数据的基于距离的迁移学习方法。我们还提供了能有效整合多个源模型的算法，并考虑到部分源模型可能比其他源模型更具辅助性。高维渐近分析从理论上阐释了源模型何时能对目标模型产生助益，并揭示了angleTL相对于其他基准方法的优越性。我们开展了大量模拟研究以验证理论结论，并展示了将angleTL应用于跨多个生物库迁移现有遗传风险预测模型的可行性。