Tractable Evaluation of Stein's Unbiased Risk Estimator with Convex Regularizers

11/11/2022

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by   Parth Nobel, et al.

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Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the ℓ_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.