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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- deep neural network
- high-dimensional classification
- minimax excess misclassification risk
- modular structure