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.

中文翻译：

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使用深度神经网络的 Minimax 最优高维分类

高维分类是高维数据分析中一个基础性的重要研究问题。在本文中，当特征维度随样本大小呈指数发散且贝叶斯分类器具有复杂的模块结构时，我们推导出极小极大过度误分类风险的非渐近率。我们还表明，基于深度神经网络的分类器可以达到上述速率，因此是极小极大最优的。