{"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/thoughts-on-massively-scalable-gaussian","title":"Thoughts on Massively Scalable Gaussian Processes","arxiv_id":"1511.01870","date":"2015-11-05","proceeding":null,"authors":["Andrew Gordon Wilson","Christoph Dann","Hannes Nickisch"],"abstract":"We introduce a framework and early results for massively scalable Gaussian\nprocesses (MSGP), significantly extending the KISS-GP approach of Wilson and\nNickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs)\non billions of datapoints, without requiring distributed inference, or severe\nassumptions. In particular, MSGP reduces the standard $O(n^3)$ complexity of GP\nlearning and inference to $O(n)$, and the standard $O(n^2)$ complexity per test\npoint prediction to $O(1)$. MSGP involves 1) decomposing covariance matrices as\nKronecker products of Toeplitz matrices approximated by circulant matrices.\nThis multi-level circulant approximation allows one to unify the orthogonal\ncomputational benefits of fast Kronecker and Toeplitz approaches, and is\nsignificantly faster than either approach in isolation; 2) local kernel\ninterpolation and inducing points to allow for arbitrarily located data inputs,\nand $O(1)$ test time predictions; 3) exploiting block-Toeplitz Toeplitz-block\nstructure (BTTB), which enables fast inference and learning when\nmultidimensional Kronecker structure is not present; and 4) projections of the\ninput space to flexibly model correlated inputs and high dimensional data. The\nability to handle many ($m \\approx n$) inducing points allows for near-exact\naccuracy and large scale kernel learning.","url_abs":"http://arxiv.org/abs/1511.01870v1","url_pdf":"http://arxiv.org/pdf/1511.01870v1.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":"thoughts-on-massively-scalable-gaussian","repo_url":"https://github.com/alshedivat/keras-gp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"thoughts-on-massively-scalable-gaussian","repo_url":"https://github.com/alshedivat/kgp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1511.01870","atlas_url":"https://app.syntology.ai/?focus=1511.01870","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}