Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions
Year: 2025
Type: preprint
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 $η$ 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).
Source: arXiv (Cornell University)
Author: Perrault, Pierre
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416243126
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