Tractable Evaluation of Stein’s Unbiased Risk Estimator with Convex Regularizers
P. Nobel, E. Candès, and S. Boyd
IEEE Transactions on Signal Processing, 71:4330–4341, 2023.
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.