Improved Bounds for Discrete Distribution Estimation Under ℓ∞ Norm
A new paper presents improved bounds for estimating discrete probability distributions under the ℓ∞ norm, including minimax bounds in expectation and high-probability tail bounds. The work resolves open questions from Kontorovich and Painsky (JMLR, 2025), providing a fully empirical version of the tightest risk bound and identifying the worst-case extremal distribution. Empirical results support the theoretical findings.
Key facts
- Improved bounds for discrete distribution estimation under ℓ∞ norm
- Includes minimax bounds in expectation and high-probability tail bounds
- Resolves open questions from Kontorovich and Painsky (JMLR, 2025)
- Provides fully empirical version of the tightest risk bound
- Identifies form of worst-case extremal distribution
- Empirical results reported
Entities
Institutions
- arXiv
- arXivLabs