Transfer learning for piecewise-constant mean estimation: optimality, l1 and l0 penalization
研究了利用源数据辅助估计分段常数信号的方法，提出了基于L1和L0惩罚的迁移学习估计器，并引入源选择算法提升性能，理论证明最优性，实验显示优于仅用目标数据的估计。
Summary We study transfer learning for estimating piecewise-constant signals when source data, which may be relevant but disparate, are available in addition to target data. We first investigate transfer learning estimators that respectively employ $ \ell_{1} $ and $ \ell_{0} $ penalties for unisource data scenarios and then generalize these estimators to accommodate multisources. To further reduce estimation errors, especially when some sources significantly differ from the target, we introduce an informative source selection algorithm. We then examine these estimators with multisource selection and establish their minimax optimality. Unlike the common narrative in the transfer learning literature that the performance is enhanced through large source sample sizes, our approaches leverage higher observational frequencies and accommodate diverse frequencies across multiple sources. Our extensive numerical experiments show that the proposed transfer learning estimators significantly improve estimation performance compared to estimators that only use the target data.