Minimax optimal high‐dimensional classification using deep neural networks

High‐dimensional classification is a fundamentally important research problem in high‐dimensional data analysis. In this paper, we derive a 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 networks can attain the above rate, hence, are minimax optimal.