[2203.03695] Learning to Bound: A Generative Cramér-Rao Bound

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arXiv:2203.03695 (cs)

[Submitted on 7 Mar 2022 (v1), last revised 9 Oct 2022 (this version, v2)]

Title:Learning to Bound: A Generative Cramér-Rao Bound

Authors:Hai Victor Habi, Hagit Messer, Yoram Bresler<br>View a PDF of the paper titled Learning to Bound: A Generative Cram\'er-Rao Bound, by Hai Victor Habi and 1 other authors

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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.

Subjects:

Machine Learning (cs.LG); Signal Processing (eess.SP)

Cite as:<br>arXiv:2203.03695 [cs.LG]

(or<br>arXiv:2203.03695v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2203.03695

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arXiv-issued DOI via DataCite

Submission history<br>From: Hai Victor Habi [view email]<br>[v1]<br>Mon, 7 Mar 2022 20:31:53 UTC (1,762 KB)

[v2]<br>Sun, 9 Oct 2022 11:25:27 UTC (2,204 KB)

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