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On Some Optimization Problems for the Rényi Divergence

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Abstract

We consider the problem of determining the maximum and minimum of the Rényi divergence Dλ(P||Q) and Dλ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.

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References

  1. Rényi, A., On Measures of Entropy and Information, Proc. 4th Berkeley Sympos. on Mathematical Statistics and Probability, Berkely, CA, USA, June 20–July 30, 1960, Neyman, J., Ed., Berkely: Univ. of California Press, 1961, vol. 1: Contributions to the Theory of Statistics, pp. 547–561.

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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

Original Russian Text © V.V. Prelov, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 3, pp. 36–53.

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.

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Prelov, V.V. On Some Optimization Problems for the Rényi Divergence. Probl Inf Transm 54, 229–244 (2018). https://doi.org/10.1134/S003294601803002X

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  • DOI: https://doi.org/10.1134/S003294601803002X

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