{"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/robust-randomized-preconditioning-for-kernel","title":"Robust, randomized preconditioning for kernel ridge regression","arxiv_id":"2304.12465","date":"2023-04-24","proceeding":null,"authors":["Mateo Díaz","Ethan N. Epperly","Zachary Frangella","Joel A. Tropp","Robert J. Webber"],"abstract":"This paper investigates two randomized preconditioning techniques for solving kernel ridge regression (KRR) problems with a medium to large number of data points ($10^4 \\leq N \\leq 10^7$), and it introduces two new methods with state-of-the-art performance. The first method, RPCholesky preconditioning, accurately solves the full-data KRR problem in $O(N^2)$ arithmetic operations, assuming sufficiently rapid polynomial decay of the kernel matrix eigenvalues. The second method, KRILL preconditioning, offers an accurate solution to a restricted version of the KRR problem involving $k \\ll N$ selected data centers at a cost of $O((N + k^2) k \\log k)$ operations. The proposed methods solve a broad range of KRR problems, making them ideal for practical applications.","url_abs":"https://arxiv.org/abs/2304.12465v4","url_pdf":"https://arxiv.org/pdf/2304.12465v4.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":"robust-randomized-preconditioning-for-kernel","repo_url":"https://github.com/eepperly/fast-efficient-krr-preconditioning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"robust-randomized-preconditioning-for-kernel","repo_url":"https://github.com/eepperly/robust-randomized-preconditioning-for-kernel-ridge-regression","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.12465","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}