# C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued Deep Learning

arXiv: https://arxiv.org/abs/2006.12590 · HTML: https://mlsanity.com/paper/2006.12590/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Improving Normalization with the James-Stein Estimator](https://mlsanity.com/paper/2312.00313/) (2023)
- [Complex-Valued Neural Networks for Data-Driven Signal Processing and Signal Understanding](https://mlsanity.com/paper/2309.07948/) (2023)
- [JojoSCL: Shrinkage Contrastive Learning for single-cell RNA sequence Clustering](https://mlsanity.com/paper/2506.00410/) (2025)

## Abstract (arXiv)

The James-Stein (JS) shrinkage estimator is a biased estimator that captures the mean of Gaussian random vectors.While it has a desirable statistical property of dominance over the maximum likelihood estimator (MLE) in terms of mean squared error (MSE), not much progress has been made on extending the estimator onto manifold-valued data. We propose C-SURE, a novel Stein's unbiased risk estimate (SURE) of the JS estimator on the manifold of complex-valued data with a theoretically proven optimum over MLE. Adapting the architecture of the complex-valued SurReal classifier, we further incorporate C-SURE into a prototype convolutional neural network (CNN) classifier. We compare C-SURE with SurReal and a real-valued baseline on complex-valued MSTAR and RadioML datasets. C-SURE is more accurate and robust than SurReal, and the shrinkage estimator is always better than MLE for the same prototype classifier. Like SurReal, C-SURE is much smaller, outperforming the real-valued baseline on MSTAR (RadioML) with less than 1 percent (3 percent) of the baseline size