Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector. We focus here on the case when the estimator minimizes a quadratic loss term plus a convex regularizer. For these estimators SURE can be evaluated analytically for a few special cases, and generically using recently developed general purpose methods for differentiating through convex optimization problems; these generic methods however do not scale to large problems. In this paper we describe methods for evaluating SURE that handle a wide class of estimators, and also scale to large problem sizes.

翻译：Stein无偏风险估计（SURE）给出了高斯随机向量均值任意估计量的$\ell_2$风险的无偏估计。本文重点研究估计量通过最小化二次损失项与凸正则化项之和得到的情形。对于此类估计量，SURE只能在少数特例下解析计算，而通用的方法则需借助近期发展的凸优化问题微分方法。但这些通用方法无法扩展至大规模问题。本文描述了一种既能处理广泛估计量类别，又可扩展至大规模问题的SURE评估方法。