Stella X. Yu : Papers / Google Scholar

C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued Deep Learning
Rudrasis Chakraborty and Yifei Xing and Minxuan Duan and Stella X. Yu
IEEE Conference on Computer Vision and Pattern Recognition Workshop: Perception Beyond the Visible Spectrum, Online, 14 June 2020
Paper | Slides


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 $1\%$ ($3\%$) of the baseline size.

complex-valued deep learning, James-Stein (JS) shrinkage estimator, Stein's unbiased risk estimate, Fr\'{e}chet Mean, prototype classifier