{"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/fast-and-flexible-admm-algorithms-for-trend","title":"Fast and Flexible ADMM Algorithms for Trend Filtering","arxiv_id":"1406.2082","date":"2014-06-09","proceeding":null,"authors":["Aaditya Ramdas","Ryan J. Tibshirani"],"abstract":"This paper presents a fast and robust algorithm for trend filtering, a\nrecently developed nonparametric regression tool. It has been shown that, for\nestimating functions whose derivatives are of bounded variation, trend\nfiltering achieves the minimax optimal error rate, while other popular methods\nlike smoothing splines and kernels do not. Standing in the way of a more\nwidespread practical adoption, however, is a lack of scalable and numerically\nstable algorithms for fitting trend filtering estimates. This paper presents a\nhighly efficient, specialized ADMM routine for trend filtering. Our algorithm\nis competitive with the specialized interior point methods that are currently\nin use, and yet is far more numerically robust. Furthermore, the proposed ADMM\nimplementation is very simple, and importantly, it is flexible enough to extend\nto many interesting related problems, such as sparse trend filtering and\nisotonic trend filtering. Software for our method is freely available, in both\nthe C and R languages.","url_abs":"http://arxiv.org/abs/1406.2082v4","url_pdf":"http://arxiv.org/pdf/1406.2082v4.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":"fast-and-flexible-admm-algorithms-for-trend","repo_url":"https://github.com/JuliaStats/Lasso.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-and-flexible-admm-algorithms-for-trend","repo_url":"https://github.com/UnofficialJuliaMirror/Lasso.jl-b4fcebef-c861-5a0f-a7e2-ba9dc32b180a","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-and-flexible-admm-algorithms-for-trend","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/Lasso.jl-b4fcebef-c861-5a0f-a7e2-ba9dc32b180a","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-and-flexible-admm-algorithms-for-trend","repo_url":"https://github.com/simonster/Lasso.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"admm","method_name":"ADMM"}],"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}