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On coupling of probability distributions and estimating the divergence through variation

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Abstract

Let X be a discrete random variable with a given probability distribution. For any α, 0 ≤ α ≤ 1, we obtain precise values for both the maximum and minimum variational distance between X and another random variable Y under which an α-coupling of these random variables is possible. We also give the maximum and minimum values for couplings of X and Y provided that the variational distance between these random variables is fixed. As a consequence, we obtain a new lower bound on the divergence through variational distance.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. V. Prelov

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  1. V. V. Prelov
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Correspondence to V. V. Prelov.

Additional information

The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

Original Russian Text © V.V. Prelov, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 3, pp. 16–22.

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Prelov, V.V. On coupling of probability distributions and estimating the divergence through variation. Probl Inf Transm 53, 215–221 (2017). https://doi.org/10.1134/S0032946017030024

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  • DOI: https://doi.org/10.1134/S0032946017030024

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