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

arXiv: https://arxiv.org/abs/2211.05947 · HTML: https://mlsanity.com/paper/2211.05947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Deep Learning Meets Adaptive Filtering: A Stein's Unbiased Risk Estimator Approach](https://mlsanity.com/paper/2307.16708/) (2023)
- [RandALO: Out-of-sample risk estimation in no time flat](https://mlsanity.com/paper/2409.09781/) (2024)

## Abstract (arXiv)

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.