A Notion of Uniqueness for the Adversarial Bayes Classifier

TL;DR

This paper introduces a new concept of uniqueness for the adversarial Bayes classifier, providing a method to compute classifiers and analyzing how regularity improves with increased perturbation, enhancing understanding of their relationship.

Contribution

It proposes a novel notion of uniqueness for adversarial Bayes classifiers and offers a simple computation procedure for one-dimensional data distributions.

Findings

Regularity of classifiers improves with larger perturbation radius

Provides a characterization linking Bayes and adversarial Bayes classifiers

Offers a method to compute all classifiers in specific data settings

Abstract

We propose a new notion of uniqueness for the adversarial Bayes classifier in the setting of binary classification. Analyzing this concept produces a simple procedure for computing all adversarial Bayes classifiers for a well-motivated family of one dimensional data distributions. This characterization is then leveraged to show that as the perturbation radius increases, certain notions of regularity for the adversarial Bayes classifiers improve. Furthermore, these results provide tools for understanding relationships between the Bayes and adversarial Bayes classifiers in one dimension.