Distribution-Free Rates in Neyman-Pearson Classification

We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $\mu_1$ is to be minimized subject to low error w.r.t. a different distribution $\mu_0$. Given a fixed VC class $\mathcal{H}$ of classifiers to be minimized over...

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Bibliographic Details
Main Authors Kalan, Mohammadreza M, Kpotufe, Samory
Format Journal Article
LanguageEnglish
Published 14.02.2024
Subjects
Computer Science - Learning
Statistics - Machine Learning
Online AccessGet full text
DOI10.48550/arxiv.2402.09560

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Summary:We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $\mu_1$ is to be minimized subject to low error w.r.t. a different distribution $\mu_0$. Given a fixed VC class $\mathcal{H}$ of classifiers to be minimized over, we provide a full characterization of possible distribution-free rates, i.e., minimax rates over the space of all pairs $(\mu_0, \mu_1)$. The rates involve a dichotomy between hard and easy classes $\mathcal{H}$ as characterized by a simple geometric condition, a three-points-separation condition, loosely related to VC dimension.
DOI:10.48550/arxiv.2402.09560