Distribution Estimation under the Infinity Norm

Aryeh Kontorovich; Amichai Painsky

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arXiv · 2402.08422

Distribution Estimation under the Infinity Norm

Aryeh Kontorovich·Amichai Painsky

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Abstract

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.

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Aryeh Kontorovich, Amichai Painsky. 2024-02-13. Distribution Estimation under the Infinity Norm. https://arxiv.org/abs/2402.08422

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