• This work is an updated version of This Paper

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 dominanceover the maximum likelihood estimator (MLE) in terms ofmean squared error (MSE), not much progress has beenmade on extending the estimator onto manifold-valued data.

We propose C-SURE, a novel Stein’s unbiased risk esti-mate (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 SurRealclassifier, 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 thesame prototype classifier. Like SurReal, C-SURE is much smaller, outperforming the real-valued baseline on MSTAR(RadioML) with less than1%(3%) of the baseline size.

• Yifei Xing
• Rudrasis Chakraborty
• Minxuan Duan
• Stella Yu

• PyTorch

• First, run cat data_split* > data_polar.zip inside the data folder.

• Next, extract data_polar.zip and set the correct path to the data_polar folder inside the argparse configuration in train_demo.py

Here is code for the baseline SurReal model that we used in the paper.

• To train the model:

python train_demo.py

The current code was prepared using single GPU. The use of multi-GPU may cause problems.

The wFM layers (SurReal) were proposed and written by Rudrasis Chakraborty, this work focuses on constructing a shrinkage layer on top of the SurReal architecture.

The use of this software is RESTRICTED to non-commercial research and educational purposes.