{"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/efficient-nonparametric-smoothness-estimation","title":"Efficient Nonparametric Smoothness Estimation","arxiv_id":"1605.05785","date":"2016-05-19","proceeding":"NeurIPS 2016 12","authors":["Shashank Singh","Simon S. Du","Barnabás Póczos"],"abstract":"Sobolev quantities (norms, inner products, and distances) of probability\ndensity functions are important in the theory of nonparametric statistics, but\nhave rarely been used in practice, partly due to a lack of practical\nestimators. They also include, as special cases, $L^2$ quantities which are\nused in many applications. We propose and analyze a family of estimators for\nSobolev quantities of unknown probability density functions. We bound the bias\nand variance of our estimators over finite samples, finding that they are\ngenerally minimax rate-optimal. Our estimators are significantly more\ncomputationally tractable than previous estimators, and exhibit a\nstatistical/computational trade-off allowing them to adapt to computational\nconstraints. We also draw theoretical connections to recent work on fast\ntwo-sample testing. Finally, we empirically validate our estimators on\nsynthetic data.","url_abs":"http://arxiv.org/abs/1605.05785v2","url_pdf":"http://arxiv.org/pdf/1605.05785v2.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":"efficient-nonparametric-smoothness-estimation","repo_url":"https://github.com/sss1/SobolevEstimation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"hypothesis-testing","task_name":"Two-sample testing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}