Tractable Evaluation of Stein’s Unbiased Risk Estimator with Convex Regularizers
P. Nobel, E. Candès, and S. Boyd
Manuscript, November 2022.
Stein's unbiased risk estimate (SURE) gives an unbiased estimate of
the 
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.