An Information-Theoretic Proof of a Finite de Finetti Theorem

Abstract

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 $n\ge k$ is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided.

5 pages. Revised version with some minor typos fixed and discussion slightly expanded