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

2022/11/11 by Nobel, Parth, Candès, Emmanuel, Boyd, Stephen · 1 citation
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2211.05947

Abstract

Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the ℓ₂ 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.

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