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Computer Science > Information Theory
Title: A Third Information-Theoretic Approach to Finite de Finetti Theorems
(Submitted on 11 Apr 2023 (this version), latest version 25 Apr 2024 (v2))
Abstract: 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.
Submission history
From: Lampros Gavalakis [view email][v1] Tue, 11 Apr 2023 17:15:48 GMT (17kb)
[v2] Thu, 25 Apr 2024 20:02:43 GMT (18kb)
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