Tight Bounds on the Binomial CDF, and the Minimum of i.i.d Binomials, in terms of KL-Divergence

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Zhu, Xiaohan, Ohannessian, Mesrob I., Srebro, Nathan
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913707433394176
author Zhu, Xiaohan
Ohannessian, Mesrob I.
Srebro, Nathan
author_facet Zhu, Xiaohan
Ohannessian, Mesrob I.
Srebro, Nathan
contents We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random variables. Both bounds are finite sample, asymptotically tight, and expressed in terms of the KL-divergence.
format Preprint
id arxiv_https___arxiv_org_abs_2502_18611
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tight Bounds on the Binomial CDF, and the Minimum of i.i.d Binomials, in terms of KL-Divergence
Zhu, Xiaohan
Ohannessian, Mesrob I.
Srebro, Nathan
Probability
Machine Learning
We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random variables. Both bounds are finite sample, asymptotically tight, and expressed in terms of the KL-divergence.
title Tight Bounds on the Binomial CDF, and the Minimum of i.i.d Binomials, in terms of KL-Divergence
topic Probability
Machine Learning
url https://arxiv.org/abs/2502.18611