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Keywords = Carlson–Levin inequality

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26 pages, 394 KiB  
Article
A Two-Moment Inequality with Applications to Rényi Entropy and Mutual Information
by Galen Reeves
Entropy 2020, 22(11), 1244; https://doi.org/10.3390/e22111244 - 1 Nov 2020
Cited by 2 | Viewed by 2854
Abstract
This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in [...] Read more.
This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions. Full article
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