An Information-Theoretic Proof of a Finite de Finetti Theorem

04/08/2021

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by   Lampros Gavalakis, et al.

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A 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 binary vector of length n≥ k is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided.