论文标题
学习绑定：生成的cramér-rao绑定
Learning to Bound: A Generative Cramér-Rao Bound
论文作者
论文摘要
Cramér-Rao Bound（CRB）是对任何无偏参数估计器的性能的众所周知的下限，已被用于研究各种各样的问题。但是，要获得CRB，需要在给定参数的可能性的可能性上进行分析表达式，或者等效地是数据的精确而明确的统计模型。在许多应用程序中，这种模型不可用。取而代之的是，这项工作引入了一种新的方法，可以使用数据驱动的方法近似CRB，从而消除了分析统计模型的要求。这种方法基于深层生成模型在建模复杂，高维分布中的最新成功。使用学习的归一化流模型，我们对测量的分布进行建模并获得CRB的近似值，我们称之为生成cramér-rao结合（GCRB）。关于简单问题的数值实验验证了这种方法，并通过学习的摄像头噪声模型对图像DeNoising和Edge检测的两个图像处理任务进行了实验，证明了其功能和好处。
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.
