An information-theoretic proof of a finite de Finetti theorem (Q2078238)

De Finetti's famous representation theorem shows that the distribution of any infinite sequence of exchangeable Bernoulli random variables may be represented as a mixture distribution over corresponding IID Bernoulli random variables. This result does not hold for finite exchangeable sequences, but there are well-known approximate versions of this result in the finite setting, giving bounds on the proximity of the distribution of the first \(k\) out of \(n\) exchangeable Bernoulli random variables and the mixture distribution one would expect from a result in the spirit of de Finetti. The main contribution of this paper is an information-theoretic proof of such a result, in which proximity of distributions is measured using Kullback-Leibler divergence. This fits in to a growing literature investigating distributional convergence from an information theory perspective in a variety of settings.