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Mathematics > Statistics Theory

arXiv:2211.05947 (math)
[Submitted on 11 Nov 2022 (v1), last revised 5 Oct 2023 (this version, v2)]

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

Authors:Parth Nobel, Emmanuel Candès, Stephen Boyd
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Abstract:Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ 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.
Comments: IEEE Transactions on Signal Processing
Subjects: Statistics Theory (math.ST); Optimization and Control (math.OC); Computation (stat.CO)
Cite as: arXiv:2211.05947 [math.ST]
  (or arXiv:2211.05947v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2211.05947

Submission history

From: Parth Nobel [view email]
[v1] Fri, 11 Nov 2022 01:48:38 UTC (37 KB)
[v2] Thu, 5 Oct 2023 18:39:54 UTC (40 KB)
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