Transfer learning for piecewise-constant mean estimation: optimality, l1 and l0 penalization
成果类型：
Article
署名作者：
Wang, F.; Yu, Y.
署名单位：
University of Warwick
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asaf018
发表日期：
2025
关键词：
摘要：
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 l(0) and l(1) 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.