[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
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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.
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)
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