{"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-log-determinants-for-gaussian","title":"Scalable Log Determinants for Gaussian Process Kernel Learning","arxiv_id":"1711.03481","date":"2017-11-09","proceeding":"NeurIPS 2017 12","authors":["Kun Dong","David Eriksson","Hannes Nickisch","David Bindel","Andrew Gordon Wilson"],"abstract":"For applications as varied as Bayesian neural networks, determinantal point\nprocesses, elliptical graphical models, and kernel learning for Gaussian\nprocesses (GPs), one must compute a log determinant of an $n \\times n$ positive\ndefinite matrix, and its derivatives - leading to prohibitive\n$\\mathcal{O}(n^3)$ computations. We propose novel $\\mathcal{O}(n)$ approaches\nto estimating these quantities from only fast matrix vector multiplications\n(MVMs). These stochastic approximations are based on Chebyshev, Lanczos, and\nsurrogate models, and converge quickly even for kernel matrices that have\nchallenging spectra. We leverage these approximations to develop a scalable\nGaussian process approach to kernel learning. We find that Lanczos is generally\nsuperior to Chebyshev for kernel learning, and that a surrogate approach can be\nhighly efficient and accurate with popular kernels.","url_abs":"http://arxiv.org/abs/1711.03481v1","url_pdf":"http://arxiv.org/pdf/1711.03481v1.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-log-determinants-for-gaussian","repo_url":"https://github.com/kd383/GPML_SLD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"scalable-log-determinants-for-gaussian","repo_url":"https://github.com/11hifish/OptSketchTraceEst","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"scalable-log-determinants-for-gaussian","repo_url":"https://github.com/ericlee0803/GP_Derivatives","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"point-processes","task_name":"Point Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1711.03481","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}