{"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/learning-to-bound-a-generative-cramer-rao","title":"Learning to Bound: A Generative Cramér-Rao Bound","arxiv_id":"2203.03695","date":"2022-03-07","proceeding":null,"authors":["Hai Victor Habi","Hagit Messer","Yoram Bresler"],"abstract":"The Cram\\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the likelihood of the measurements given the parameters, or equivalently a precise and explicit statistical model for the data. In many applications, such a model is not available. Instead, this work introduces a novel approach to approximate the CRB using data-driven methods, which removes the requirement for an analytical statistical model. This approach is based on the recent success of deep generative models in modeling complex, high-dimensional distributions. Using a learned normalizing flow model, we model the distribution of the measurements and obtain an approximation of the CRB, which we call Generative Cram\\'er-Rao Bound (GCRB). Numerical experiments on simple problems validate this approach, and experiments on two image processing tasks of image denoising and edge detection with a learned camera noise model demonstrate its power and benefits.","url_abs":"https://arxiv.org/abs/2203.03695v2","url_pdf":"https://arxiv.org/pdf/2203.03695v2.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":"learning-to-bound-a-generative-cramer-rao","repo_url":"https://github.com/haihabi/generativecrb","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"edge-detection","task_name":"Edge Detection"},{"task_slug":"image-denoising","task_name":"Image Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}