Sharper Perturbed-Kullback-Leibler Exponential Tail Bounds for Beta and Dirichlet Distributions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909732338401280 |
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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 |