{"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/smoothed-residual-stopping-for-statistical","title":"Smoothed residual stopping for statistical inverse problems via truncated SVD estimation","arxiv_id":"1909.13702","date":"2019-09-30","proceeding":null,"authors":["Bernhard Stankewitz"],"abstract":"This work examines under what circumstances adaptivity for truncated SVD estimation can be achieved by an early stopping rule based on the smoothed residuals $ \\| ( A A^{\\top} )^{\\alpha / 2} ( Y - A \\hat{\\mu}^{( m )}) \\|^{2} $. Lower and upper bounds for the risk are derived, which show that moderate smoothing of the residuals can be used to adapt over classes of signals with varying smoothness, while oversmoothing yields suboptimal convergence rates. The theoretical results are illustrated by Monte-Carlo simulations.","url_abs":"https://arxiv.org/abs/1909.13702v2","url_pdf":"https://arxiv.org/pdf/1909.13702v2.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":"smoothed-residual-stopping-for-statistical","repo_url":"https://github.com/be5tan/rlystop","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}