{"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/gaussian-process-kernels-for-pattern","title":"Gaussian Process Kernels for Pattern Discovery and Extrapolation","arxiv_id":"1302.4245","date":"2013-02-18","proceeding":null,"authors":["Andrew Gordon Wilson","Ryan Prescott Adams"],"abstract":"Gaussian processes are rich distributions over functions, which provide a\nBayesian nonparametric approach to smoothing and interpolation. We introduce\nsimple closed form kernels that can be used with Gaussian processes to discover\npatterns and enable extrapolation. These kernels are derived by modelling a\nspectral density -- the Fourier transform of a kernel -- with a Gaussian\nmixture. The proposed kernels support a broad class of stationary covariances,\nbut Gaussian process inference remains simple and analytic. We demonstrate the\nproposed kernels by discovering patterns and performing long range\nextrapolation on synthetic examples, as well as atmospheric CO2 trends and\nairline passenger data. We also show that we can reconstruct standard\ncovariances within our framework.","url_abs":"http://arxiv.org/abs/1302.4245v3","url_pdf":"http://arxiv.org/pdf/1302.4245v3.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":"gaussian-process-kernels-for-pattern","repo_url":"https://github.com/icsm/pgmuvi","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"gaussian-process-kernels-for-pattern","repo_url":"https://github.com/SimonRennotte/GaussianProcessPatternDiscovery","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1302.4245","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}