Optimal exponential bounds on the accuracy of classification

TL;DR

This paper derives optimal exponential bounds for the accuracy of binary classifiers, linking performance guarantees to distribution complexity and margin parameters, advancing theoretical understanding of classification limits.

Contribution

It provides new exponential bounds on minimax accuracy confidence functions, incorporating distribution complexity and margin effects, which were not previously fully characterized.

Findings

Derived optimal exponential bounds on classifier accuracy

Linked bounds to distribution complexity via entropy exponents

Analyzed dependence on margin parameters

Abstract

We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence function based on the excess risk. We study how this quantity depends on the complexity of the class of distributions characterized by exponents of entropies of the class of regression functions or of the class of Bayes classifiers corresponding to the distributions from the class. We also study its dependence on margin parameters of the classification problem.