Distribution Estimation under the Infinity Norm
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911776298237952 |
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| author | Kontorovich, Aryeh Painsky, Amichai |
| author_facet | Kontorovich, Aryeh Painsky, Amichai |
| contents | We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees for the maximum likelihood estimator significantly improve upon the currently known results. A variety of techniques are utilized and innovated upon, including Chernoff-type inequalities and empirical Bernstein bounds. We illustrate our results in synthetic and real-world experiments. Finally, we apply our proposed framework to a basic selective inference problem, where we estimate the most frequent probabilities in a sample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution Estimation under the Infinity Norm Kontorovich, Aryeh Painsky, Amichai Statistics Theory Machine Learning We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees for the maximum likelihood estimator significantly improve upon the currently known results. A variety of techniques are utilized and innovated upon, including Chernoff-type inequalities and empirical Bernstein bounds. We illustrate our results in synthetic and real-world experiments. Finally, we apply our proposed framework to a basic selective inference problem, where we estimate the most frequent probabilities in a sample. |
| title | Distribution Estimation under the Infinity Norm |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2402.08422 |