TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression

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.

AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression

We consider the transfer learning problem in the high dimensional setting, where the feature dimension is larger than the sample size. To learn transferable information, which may vary across features or the source samples, we propose an adaptive transfer learning method that can detect and aggregate the feature-wise (F-AdaTrans) or sample-wise (S-AdaTrans) transferable structures. We achieve this by employing a novel fused-penalty, coupled with weights that can adapt according to the transferable structure. To choose the weight, we propose a theoretically informed, data-driven procedure, enabling F-AdaTrans to selectively fuse the transferable signals with the target while filtering out non-transferable signals, and S-AdaTrans to obtain the optimal combination of information transferred from each source sample. The non-asymptotic rates are established, which recover existing near-minimax optimal rates in special cases. The effectiveness of the proposed method is validated using both synthetic and real data.