{"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/multivariate-regression-and-fit-function","title":"Multivariate regression and fit function uncertainty","arxiv_id":"1310.1022","date":"2013-10-03","proceeding":null,"authors":["Peter Kovesarki","Ian C. Brock"],"abstract":"This article describes a multivariate polynomial regression method where the\nuncertainty of the input parameters are approximated with Gaussian\ndistributions, derived from the central limit theorem for large weighted sums,\ndirectly from the training sample. The estimated uncertainties can be\npropagated into the optimal fit function, as an alternative to the statistical\nbootstrap method. This uncertainty can be propagated further into a loss\nfunction like quantity, with which it is possible to calculate the expected\nloss function, and allows to select the optimal polynomial degree with\nstatistical significance. Combined with simple phase space splitting methods,\nit is possible to model most features of the training data even with low degree\npolynomials or constants.","url_abs":"http://arxiv.org/abs/1310.1022v1","url_pdf":"http://arxiv.org/pdf/1310.1022v1.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":"multivariate-regression-and-fit-function","repo_url":"https://github.com/freemeson/multinomial","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}