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 is close to a mixture of product distributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided.
Funding Statement
L.G. was supported in part by EPSRC grant number RG94782. I.K. was supported in part by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant,” project number 1034.
Acknowledgments
We thank Sergio Verdú and an anonymous referee for useful suggestions regarding the presentation of the results in this paper.
Citation
Lampros Gavalakis. Ioannis Kontoyiannis. "An information-theoretic proof of a finite de Finetti theorem." Electron. Commun. Probab. 26 1 - 5, 2021. https://doi.org/10.1214/21-ECP428
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