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arXiv · 2605.30509

Improved Distribution Estimation in $\ell_\infty$

Doron Cohen·Aryeh Kontorovich·Yonatan Livshitz
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Abstract

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.

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Doron Cohen, Aryeh Kontorovich, Yonatan Livshitz. 2026-05-28. Improved Distribution Estimation in $\ell_\infty$. https://arxiv.org/abs/2605.30509

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