A Generative Cramér-Rao Bound

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.

Computer Science Machine Learning Submitted on 7 Mar 2022 v1 https://arxiv.org/abs/2203.03695v1 , last revised 9 Oct 2022 this version, v2 Title:Learning to Bound: A Generative Cramér-Rao Bound View PDF /pdf/2203.03695 HTML experimental https://arxiv.org/html/2203.03695v2 Abstract: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. Submission history From: Hai Victor Habi view email /show-email/e9f6d25a/2203.03695 Mon, 7 Mar 2022 20:31:53 UTC 1,762 KB v1 /abs/2203.03695v1 v2 Sun, 9 Oct 2022 11:25:27 UTC 2,204 KB Current browse context: cs.LG References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both 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. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .