A Third Information-Theoretic Approach to Finite de Finetti Theorems
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929327668461568 |
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| author | Berta, Mario Gavalakis, Lampros Kontoyiannis, Ioannis |
| author_facet | Berta, Mario Gavalakis, Lampros Kontoyiannis, Ioannis |
| contents | A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided. This bound is tighter than those obtained via earlier information-theoretic proofs, and its utility extends to random variables taking values in general spaces. The core argument employed has its origins in the quantum information-theoretic literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05360 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Third Information-Theoretic Approach to Finite de Finetti Theorems Berta, Mario Gavalakis, Lampros Kontoyiannis, Ioannis Information Theory Probability Quantum Physics A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided. This bound is tighter than those obtained via earlier information-theoretic proofs, and its utility extends to random variables taking values in general spaces. The core argument employed has its origins in the quantum information-theoretic literature. |
| title | A Third Information-Theoretic Approach to Finite de Finetti Theorems |
| topic | Information Theory Probability Quantum Physics |
| url | https://arxiv.org/abs/2304.05360 |