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Mutual information of several random variables and its estimation via variation

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Abstract

We obtain some upper and lower bounds for the maximum of mutual information of several random variables via variational distance between the joint distribution of these random variables and the product of its marginal distributions. In this connection, some properties of variational distance between probability distributions of this type are derived. We show that in some special cases estimates of the maximum of mutual information obtained here are optimal or asymptotically optimal. Some results of this paper generalize the corresponding results of [1–3] to the multivariate case.

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References

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    V. V. Prelov

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

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Original Russian Text © V.V. Prelov, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 4, pp. 3–17.

Supported in part by the Russian Foundation for Basic Research, project no. 09-01-00536.

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Prelov, V.V. Mutual information of several random variables and its estimation via variation. Probl Inf Transm 45, 295–308 (2009). https://doi.org/10.1134/S0032946009040012

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