Distribution-Free Rates in Neyman-Pearson Classification
<|reference_start|>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, 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.<|reference_end|>
@article{kalan2024distribution-free,
    title={Distribution-Free Rates in Neyman-Pearson Classification},
    author={Mohammadreza M. Kalan, Samory Kpotufe},
    journal={arXiv preprint arXiv:2402.09560},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09560},
    primaryClass={cs.LG stat.ML}
}