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.

翻译：高维分类是高维数据分析中一个基本且重要的研究问题。本文在特征维数随样本量呈指数增长且贝叶斯分类器具有复杂模块化结构的情况下，推导了极小极大超额误分类风险的非渐近率。我们还证明了基于深度神经网络的分类器能够达到上述率，因此具有极小极大最优性。