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

TL;DR

AdaTrans introduces adaptive transfer learning methods for high-dimensional linear regression, effectively identifying and aggregating transferable features or samples to improve estimation accuracy in complex settings.

Contribution

The paper proposes novel feature-wise and sample-wise adaptive transfer learning methods with data-driven weight selection, enhancing transferability detection and achieving near-oracle convergence rates.

Findings

F-AdaTrans achieves near-oracle convergence rates.

S-AdaTrans recovers near-minimax optimal rates.

Validated through simulations and real data, outperforming existing methods.

Abstract

We consider the transfer learning problem in the high dimensional linear regression 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 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. We show that, with appropriately chosen weights, F-AdaTrans achieves a convergence rate close to that of an oracle estimator with a known transferable structure, and S-AdaTrans recovers existing near-minimax optimal rates as a special case. The effectiveness of the proposed method is validated using both simulation and real data, demonstrating favorable performance compared to the existing methods.