{"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/non-stationary-spectral-kernels","title":"Non-Stationary Spectral Kernels","arxiv_id":"1705.08736","date":"2017-05-24","proceeding":"NeurIPS 2017 12","authors":["Sami Remes","Markus Heinonen","Samuel Kaski"],"abstract":"We propose non-stationary spectral kernels for Gaussian process regression.\nWe propose to model the spectral density of a non-stationary kernel function as\na mixture of input-dependent Gaussian process frequency density surfaces. We\nsolve the generalised Fourier transform with such a model, and present a family\nof non-stationary and non-monotonic kernels that can learn input-dependent and\npotentially long-range, non-monotonic covariances between inputs. We derive\nefficient inference using model whitening and marginalized posterior, and show\nwith case studies that these kernels are necessary when modelling even rather\nsimple time series, image or geospatial data with non-stationary\ncharacteristics.","url_abs":"http://arxiv.org/abs/1705.08736v1","url_pdf":"http://arxiv.org/pdf/1705.08736v1.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":"non-stationary-spectral-kernels","repo_url":"https://github.com/sremes/nonstationary-spectral-kernels","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1705.08736","atlas_url":"https://app.syntology.ai/?focus=1705.08736","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}