Analyzing High Dimensional Covariance Matrices Using Methods in Deep Learning

Covariance matrix estimation is important in many statistical methods and applications. For example, it is applied in asset allocation, classification of human tumors based on gene expression arrays, and many others. Various classes of models have been proposed in the literature to address the problem. However, the traditional statistical methods become quite weak when the dimensional of the data becomes large. Although some dimension reduction methods have been introduced, the performances are still not acceptable. In our research, we will try to use some methods in deep learning to address such a problem. Our initial results are quite good, beating the traditional statistical methods easily considering the prediction accuracy. To give a comprehensive comparison of our methods to the traditional methods, we need to conduct a lot of experiments, which need the help of GPU server(GPU is much faster for deep learning models than CPU).