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.

翻译：我们考虑高维场景下的迁移学习问题，其中特征维度大于样本量。为捕捉可能随特征或源样本变化的可迁移信息，我们提出一种自适应迁移学习方法，能够检测并聚合特征级（F-AdaTrans）或样本级（S-AdaTrans）的可迁移结构。通过采用一种融合惩罚项并结合可根据可迁移结构自适应调整的权重来实现这一目标。为选择权重，我们提出一种基于理论指导的数据驱动流程，使F-AdaTrans能够选择性地将可迁移信号与目标信号融合，同时过滤掉不可迁移信号，而S-AdaTrans则获得从每个源样本迁移信息的最优组合。本文建立了非渐近收敛速率，在特殊情形下可恢复现有近极小化最优速率。通过合成数据与真实数据验证了所提方法的有效性。