Improved Distribution Estimation in $\ell_\infty$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911729498193920 |
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| author | Cohen, Doron Kontorovich, Aryeh Livshitz, Yonatan |
| author_facet | Cohen, Doron Kontorovich, Aryeh Livshitz, Yonatan |
| contents | We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30509 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Distribution Estimation in $\ell_\infty$ Cohen, Doron Kontorovich, Aryeh Livshitz, Yonatan Machine Learning Artificial Intelligence We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well. |
| title | Improved Distribution Estimation in $\ell_\infty$ |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.30509 |