{"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/preconditioning-kernel-matrices","title":"Preconditioning Kernel Matrices","arxiv_id":"1602.06693","date":"2016-02-22","proceeding":null,"authors":["Kurt Cutajar","Michael A. Osborne","John P. Cunningham","Maurizio Filippone"],"abstract":"The computational and storage complexity of kernel machines presents the\nprimary barrier to their scaling to large, modern, datasets. A common way to\ntackle the scalability issue is to use the conjugate gradient algorithm, which\nrelieves the constraints on both storage (the kernel matrix need not be stored)\nand computation (both stochastic gradients and parallelization can be used).\nEven so, conjugate gradient is not without its own issues: the conditioning of\nkernel matrices is often such that conjugate gradients will have poor\nconvergence in practice. Preconditioning is a common approach to alleviating\nthis issue. Here we propose preconditioned conjugate gradients for kernel\nmachines, and develop a broad range of preconditioners particularly useful for\nkernel matrices. We describe a scalable approach to both solving kernel\nmachines and learning their hyperparameters. We show this approach is exact in\nthe limit of iterations and outperforms state-of-the-art approximations for a\ngiven computational budget.","url_abs":"http://arxiv.org/abs/1602.06693v2","url_pdf":"http://arxiv.org/pdf/1602.06693v2.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":"preconditioning-kernel-matrices","repo_url":"https://github.com/mauriziofilippone/preconditioned_GPs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1602.06693","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}