{"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/tight-bounds-for-minimum-l1-norm","title":"Tight bounds for minimum l1-norm interpolation of noisy data","arxiv_id":"2111.05987","date":"2021-11-10","proceeding":null,"authors":["Guillaume Wang","Konstantin Donhauser","Fanny Yang"],"abstract":"We provide matching upper and lower bounds of order $\\sigma^2/\\log(d/n)$ for the prediction error of the minimum $\\ell_1$-norm interpolator, a.k.a. basis pursuit. Our result is tight up to negligible terms when $d \\gg n$, and is the first to imply asymptotic consistency of noisy minimum-norm interpolation for isotropic features and sparse ground truths. Our work complements the literature on \"benign overfitting\" for minimum $\\ell_2$-norm interpolation, where asymptotic consistency can be achieved only when the features are effectively low-dimensional.","url_abs":"https://arxiv.org/abs/2111.05987v2","url_pdf":"https://arxiv.org/pdf/2111.05987v2.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":"abstracts"},"code_links":[{"paper_slug":"tight-bounds-for-minimum-l1-norm","repo_url":"https://github.com/DonhauserK/DonhauserK.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2111.05987","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}