A Notion of Uniqueness for the Adversarial Bayes Classifier

2024/04/25 by Natalie S. Frank, Frank, Natalie S. · 1 citation
Computer Science · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2404.16956

openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

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• Adversarial Surrogate Risk Bounds for Binary Classification

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