{"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/rapid-and-deterministic-estimation-of","title":"Rapid and deterministic estimation of probability densities using scale-free field theories","arxiv_id":"1312.6661","date":"2013-12-23","proceeding":null,"authors":["Justin B. Kinney"],"abstract":"The question of how best to estimate a continuous probability density from\nfinite data is an intriguing open problem at the interface of statistics and\nphysics. Previous work has argued that this problem can be addressed in a\nnatural way using methods from statistical field theory. Here I describe new\nresults that allow this field-theoretic approach to be rapidly and\ndeterministically computed in low dimensions, making it practical for use in\nday-to-day data analysis. Importantly, this approach does not impose a\nprivileged length scale for smoothness of the inferred probability density, but\nrather learns a natural length scale from the data due to the tradeoff between\ngoodness-of-fit and an Occam factor. Open source software implementing this\nmethod in one and two dimensions is provided.","url_abs":"http://arxiv.org/abs/1312.6661v3","url_pdf":"http://arxiv.org/pdf/1312.6661v3.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":"rapid-and-deterministic-estimation-of","repo_url":"https://github.com/jbkinney/13_deft","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}