Minimax optimal high-dimensional classification using deep neural networks

Abstract

High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive nonasymptotic rate for the minimax excess misclassification risk when feature dimension exponentially diverges with the sample size and the Bayes classifier possesses a complicated modular structure. We also show that classifiers based on deep neural network attain the above rate, hence, are minimax optimal.