Minimax optimal high-dimensional classification using deep neural networks

Shuoyang Wang, Zuofeng Shang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article numbere482
Issue number1
StatePublished - Dec 2022

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


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