{"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/implicit-manifold-gaussian-process-regression","title":"Implicit Manifold Gaussian Process Regression","arxiv_id":"2310.19390","date":"2023-10-30","proceeding":"NeurIPS 2023 11","authors":["Bernardo Fichera","Viacheslav Borovitskiy","Andreas Krause","Aude Billard"],"abstract":"Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this technique to higher dimensions is to leverage the implicit low-dimensional manifold upon which the data actually lies, as postulated by the manifold hypothesis. Prior work ordinarily requires the manifold structure to be explicitly provided though, i.e. given by a mesh or be known to be one of the well-known manifolds like the sphere. In contrast, in this paper we propose a Gaussian process regression technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way. For the resulting model, we discuss its convergence to the Mat\\'ern Gaussian process on the assumed manifold. Our technique scales up to hundreds of thousands of data points, and may improve the predictive performance and calibration of the standard Gaussian process regression in high-dimensional settings.","url_abs":"https://arxiv.org/abs/2310.19390v2","url_pdf":"https://arxiv.org/pdf/2310.19390v2.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":"implicit-manifold-gaussian-process-regression","repo_url":"https://github.com/nash169/manifold-gp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}