{"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/empirical-non-parametric-estimation-of-the","title":"Empirical non-parametric estimation of the Fisher Information","arxiv_id":"1408.1182","date":"2014-08-06","proceeding":null,"authors":["Visar Berisha","Alfred O. Hero"],"abstract":"The Fisher information matrix (FIM) is a foundational concept in statistical\nsignal processing. The FIM depends on the probability distribution, assumed to\nbelong to a smooth parametric family. Traditional approaches to estimating the\nFIM require estimating the probability distribution function (PDF), or its\nparameters, along with its gradient or Hessian. However, in many practical\nsituations the PDF of the data is not known but the statistician has access to\nan observation sample for any parameter value. Here we propose a method of\nestimating the FIM directly from sampled data that does not require knowledge\nof the underlying PDF. The method is based on non-parametric estimation of an\n$f$-divergence over a local neighborhood of the parameter space and a relation\nbetween curvature of the $f$-divergence and the FIM. Thus we obtain an\nempirical estimator of the FIM that does not require density estimation and is\nasymptotically consistent. We empirically evaluate the validity of our approach\nusing two experiments.","url_abs":"http://arxiv.org/abs/1408.1182v2","url_pdf":"http://arxiv.org/pdf/1408.1182v2.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":"empirical-non-parametric-estimation-of-the","repo_url":"https://github.com/pkadambi/Bootstrapped-Nonparmetrics","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}