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Bibliographic Details
Main Author: Perrault, Pierre
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.07991
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author Perrault, Pierre
author_facet Perrault, Pierre
contents This paper presents an improved exponential tail bound for Beta distributions, refining a result in [15]. This improvement is achieved by interpreting their bound as a regular Kullback-Leibler (KL) divergence one, while introducing a specific perturbation $η$ that shifts the mean of the Beta distribution closer to zero within the KL bound. Our contribution is to show that a larger perturbation can be chosen, thereby tightening the bound. We then extend this result from the Beta distribution to Dirichlet distributions and Dirichlet processes (DPs).
format Preprint
id arxiv_https___arxiv_org_abs_2508_07991
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions
Perrault, Pierre
Probability
Machine Learning
This paper presents an improved exponential tail bound for Beta distributions, refining a result in [15]. This improvement is achieved by interpreting their bound as a regular Kullback-Leibler (KL) divergence one, while introducing a specific perturbation $η$ that shifts the mean of the Beta distribution closer to zero within the KL bound. Our contribution is to show that a larger perturbation can be chosen, thereby tightening the bound. We then extend this result from the Beta distribution to Dirichlet distributions and Dirichlet processes (DPs).
title Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions
topic Probability
Machine Learning
url https://arxiv.org/abs/2508.07991