{"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/know-your-boundaries-constraining-gaussian","title":"Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features","arxiv_id":"1904.05207","date":"2019-04-10","proceeding":null,"authors":["Arno Solin","Manon Kok"],"abstract":"Gaussian processes (GPs) provide a powerful framework for extrapolation,\ninterpolation, and noise removal in regression and classification. This paper\nconsiders constraining GPs to arbitrarily-shaped domains with boundary\nconditions. We solve a Fourier-like generalised harmonic feature representation\nof the GP prior in the domain of interest, which both constrains the GP and\nattains a low-rank representation that is used for speeding up inference. The\nmethod scales as $\\mathcal{O}(nm^2)$ in prediction and $\\mathcal{O}(m^3)$ in\nhyperparameter learning for regression, where $n$ is the number of data points\nand $m$ the number of features. Furthermore, we make use of the variational\napproach to allow the method to deal with non-Gaussian likelihoods. The\nexperiments cover both simulated and empirical data in which the boundary\nconditions allow for inclusion of additional physical information.","url_abs":"http://arxiv.org/abs/1904.05207v1","url_pdf":"http://arxiv.org/pdf/1904.05207v1.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":"know-your-boundaries-constraining-gaussian","repo_url":"https://github.com/AaltoML/boundary-gp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1904.05207","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}