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

Parth Nobel, Emmanuel Candes, Stephen Boyd

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.