Distribution-Free Rates in Neyman-Pearson Classification
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909107185778688 |
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| author | Kalan, Mohammadreza M. Kpotufe, Samory |
| author_facet | Kalan, Mohammadreza M. Kpotufe, Samory |
| contents | We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $μ_1$ is to be minimized subject to low error w.r.t. a different distribution $μ_0$. 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 $(μ_0, μ_1)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution-Free Rates in Neyman-Pearson Classification Kalan, Mohammadreza M. Kpotufe, Samory Machine Learning We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $μ_1$ is to be minimized subject to low error w.r.t. a different distribution $μ_0$. 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 $(μ_0, μ_1)$. 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. |
| title | Distribution-Free Rates in Neyman-Pearson Classification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.09560 |