{"ID":2883753,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.07991","arxiv_id":"2508.07991","title":"Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions","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).","short_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...","url_abs":"https://arxiv.org/abs/2508.07991","url_pdf":"https://arxiv.org/pdf/2508.07991v1","authors":"[\"Pierre Perrault\"]","published":"2025-08-11T13:53:55Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"cs.LG\"]","methods":"[]","has_code":false}