mlsanityData to 14 Oct 2026

Improved Distribution Estimation in ℓ_∞

arXiv 2605.30509 ↗First posted 28 May 2026stat.ML cs.AI cs.LGcited by 0

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Abstract (arXiv)

We present improved bounds for estimating discrete probability distributions under the ℓ_∞ 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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 3 of its 8 references that are in the map. First posted on arXiv 28 May 2026.

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3 of 8 references.

References · 3

  1. 2018On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variablescited by 19
  2. 2024Distribution Estimation under the Infinity Normcited by 2
  3. 2024The Empirical Mean is Minimax Optimal for Local Glivenko-Cantellicited by 2

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