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.

我们提出了一种自适应迁移学习方法，可以在高维环境中处理特征维度大于样本大小的情况。通过使用一种新型的融合罚函数，配合能够根据可迁移结构自适应调整的权重，我们能够检测和聚合特征层面或样本层面的可迁移结构，从而选择性地融合可迁移信号并过滤掉不可迁移信号。此方法的有效性已经通过合成数据和真实数据的验证得到证明。