Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions

Pierre Perrault

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arXiv · 2508.07991

Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions

Pierre Perrault

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Abstract

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 $\eta$ 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).

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Pierre Perrault. 2025-08-11. Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions. https://arxiv.org/abs/2508.07991

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