{"slug": "a-generative-cramer-rao-bound", "title": "A Generative Cramér-Rao Bound", "summary": "Researchers at Tel Aviv University introduced the Generative Cramér-Rao Bound (GCRB), a data-driven method that approximates the classical Cramér-Rao bound using deep generative models, eliminating the need for an analytical statistical model. The approach, presented in a paper submitted on 7 Mar 2022 and revised on 9 Oct 2022, uses a learned normalizing flow to model measurement distributions, and numerical experiments on image denoising and edge detection with a learned camera noise model demonstrated its effectiveness.", "body_md": "# Computer Science > Machine Learning\n\n[Submitted on 7 Mar 2022 (\n\n[v1](https://arxiv.org/abs/2203.03695v1)), last revised 9 Oct 2022 (this version, v2)]# Title:Learning to Bound: A Generative Cramér-Rao Bound\n\n[View PDF](/pdf/2203.03695)\n\n[HTML (experimental)](https://arxiv.org/html/2203.03695v2)\n\nAbstract:The Cramér-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 Cramér-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.\n\n## Submission history\n\nFrom: Hai Victor Habi [[view email](/show-email/e9f6d25a/2203.03695)]\n\n**Mon, 7 Mar 2022 20:31:53 UTC (1,762 KB)**\n\n[[v1]](/abs/2203.03695v1)**[v2]** Sun, 9 Oct 2022 11:25:27 UTC (2,204 KB)\n\n### Current browse context:\n\ncs.LG\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/a-generative-cramer-rao-bound", "canonical_source": "https://arxiv.org/abs/2203.03695", "published_at": "2026-08-16 10:06:48+00:00", "updated_at": "2026-08-16 10:40:45.725234+00:00", "lang": "en", "topics": ["machine-learning", "generative-ai"], "entities": ["Tel Aviv University", "Generative Cramér-Rao Bound", "Cramér-Rao bound", "normalizing flow"], "alternates": {"html": "https://wpnews.pro/news/a-generative-cramer-rao-bound", "markdown": "https://wpnews.pro/news/a-generative-cramer-rao-bound.md", "text": "https://wpnews.pro/news/a-generative-cramer-rao-bound.txt", "jsonld": "https://wpnews.pro/news/a-generative-cramer-rao-bound.jsonld"}}