{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/transfer-learning-for-piecewise-constant-mean","title":"Transfer learning for piecewise-constant mean estimation: Optimality, $\\ell_1$- and $\\ell_0$-penalisation","arxiv_id":"2310.05646","date":"2023-10-09","proceeding":null,"authors":["Fan Wang","Yi Yu"],"abstract":"We study transfer learning for estimating piecewise-constant signals when source data, which may be relevant but disparate, are available in addition to the target data. We first investigate transfer learning estimators that respectively employ $\\ell_1$- and $\\ell_0$-penalties for unisource data scenarios and then generalise 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 observation frequencies and accommodate diverse frequencies across multiple sources. Our theoretical findings are supported by extensive numerical experiments, with the code available online, see https://github.com/chrisfanwang/transferlearning","url_abs":"https://arxiv.org/abs/2310.05646v4","url_pdf":"https://arxiv.org/pdf/2310.05646v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"transfer-learning-for-piecewise-constant-mean","repo_url":"https://github.com/chrisfanwang/transferlearning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}