{"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/learning-integral-representations-of-gaussian","title":"Learning Integral Representations of Gaussian Processes","arxiv_id":"1802.07528","date":"2018-02-21","proceeding":null,"authors":["Zilong Tan","Sayan Mukherjee"],"abstract":"We propose a representation of Gaussian processes (GPs) based on powers of\nthe integral operator defined by a kernel function, we call these stochastic\nprocesses integral Gaussian processes (IGPs). Sample paths from IGPs are\nfunctions contained within the reproducing kernel Hilbert space (RKHS) defined\nby the kernel function, in contrast sample paths from the standard GP are not\nfunctions within the RKHS. We develop computationally efficient non-parametric\nregression models based on IGPs. The main innovation in our regression\nalgorithm is the construction of a low dimensional subspace that captures the\ninformation most relevant to explaining variation in the response. We use ideas\nfrom supervised dimension reduction to compute this subspace. The result of\nusing the construction we propose involves significant improvements in the\ncomputational complexity of estimating kernel hyper-parameters as well as\nreducing the prediction variance.","url_abs":"http://arxiv.org/abs/1802.07528v4","url_pdf":"http://arxiv.org/pdf/1802.07528v4.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":"learning-integral-representations-of-gaussian","repo_url":"https://github.com/ZilongTan/sigp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}