{"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/scalable-gaussian-processes-with-grid-1","title":"Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)","arxiv_id":"1807.02125","date":"2018-07-05","proceeding":"ICML 2018","authors":["Trefor W. Evans","Prasanth B. Nair"],"abstract":"We introduce a kernel approximation strategy that enables computation of the\nGaussian process log marginal likelihood and all hyperparameter derivatives in\n$\\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found\nusing a Nystrom approximation from a dense Cartesian product grid of inducing\npoints. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor\nproducts, computational complexity of the training procedure can be practically\nindependent of the number of inducing points. This allows us to use arbitrarily\nmany inducing points to achieve a globally accurate kernel approximation, even\nin high-dimensional problems. The fast likelihood evaluation enables type-I or\nII Bayesian inference on large-scale datasets. We benchmark our algorithms on\nreal-world problems with up to two-million training points and $10^{33}$\ninducing points.","url_abs":"http://arxiv.org/abs/1807.02125v2","url_pdf":"http://arxiv.org/pdf/1807.02125v2.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":"scalable-gaussian-processes-with-grid-1","repo_url":"https://github.com/treforevans/gp_grief","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"scalable-gaussian-processes-with-grid-1","repo_url":"https://github.com/treforevans/uci_datasets","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.02125","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}