TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression
This addresses covariate-shift robustness in transfer learning for high-dimensional regression, which is an incremental improvement over existing methods.
The paper tackles transfer learning for high-dimensional regression under both model shifts and covariate shifts by proposing a two-step method with a fused-regularizer, achieving robustness to covariate shifts with nonasymptotic error bounds and minimax-optimality under certain conditions.
The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this work, we tackle model shifts in the presence of covariate shifts in the high-dimensional regression setting. Specifically, we propose a two-step method with a novel fused-regularizer that effectively leverages samples from source tasks to improve the learning performance on a target task with limited samples. Nonasymptotic bound is provided for the estimation error of the target model, showing the robustness of the proposed method to covariate shifts. We further establish conditions under which the estimator is minimax-optimal. Additionally, we extend the method to a distributed setting, allowing for a pretraining-finetuning strategy, requiring just one round of communication while retaining the estimation rate of the centralized version. Numerical tests validate our theory, highlighting the method's robustness to covariate shifts.