Relative entropy bounds for sampling with and without replacement
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909989134663680 |
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| author | Johnson, Oliver Gavalakis, Lampros Kontoyiannis, Ioannis |
| author_facet | Johnson, Oliver Gavalakis, Lampros Kontoyiannis, Ioannis |
| contents | Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and, unlike previous results, they depend on the number of balls of each colour in the urn. The connection of these results with finite de Finetti-style theorems is explored, and it is observed that a sampling bound due to Stam (1978) combined with the convexity of relative entropy yield a new finite de Finetti bound in relative entropy, which achieves the optimal asymptotic convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative entropy bounds for sampling with and without replacement Johnson, Oliver Gavalakis, Lampros Kontoyiannis, Ioannis Probability Information Theory 60E05 (Primary) 60G09 (Secondary) Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and, unlike previous results, they depend on the number of balls of each colour in the urn. The connection of these results with finite de Finetti-style theorems is explored, and it is observed that a sampling bound due to Stam (1978) combined with the convexity of relative entropy yield a new finite de Finetti bound in relative entropy, which achieves the optimal asymptotic convergence rate. |
| title | Relative entropy bounds for sampling with and without replacement |
| topic | Probability Information Theory 60E05 (Primary) 60G09 (Secondary) |
| url | https://arxiv.org/abs/2404.06632 |