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

TL;DR

This paper introduces C-SURE, a novel shrinkage estimator for complex-valued data, integrated into a prototype CNN classifier, demonstrating superior accuracy and robustness over existing methods on radar and radio datasets.

Contribution

It extends the James-Stein shrinkage estimator to complex-valued data on manifolds and incorporates it into a prototype CNN classifier for improved performance.

Findings

C-SURE outperforms SurReal and real-valued baselines in accuracy.

C-SURE is more robust and smaller in size.

Shrinkage estimator consistently better than MLE for the same classifier.

Abstract

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