Learning to Bound: A Generative Cramér-Rao Bound

The Cramér-Rao bound (CRB), a well-known lower on the performance of any unbiased parameter estimator, has been used to study wide variety problems. However, obtain CRB, requires an analytical expression for likelihood measurements given parameters, or equivalently precise and explicit statistical model data. In many applications, such is not available. Instead, this work introduces novel approach approximate CRB using data-driven methods, which removes requirement model. This based recent success deep generative models in modeling complex, high-dimensional distributions. Using learned normalizing flow model, we distribution approximation call Generative Bound (GCRB). Numerical experiments simple problems validate approach, two image processing tasks denoising edge detection with camera noise demonstrate its power benefits.