Two-Moment Inequalities for R\'enyi Entropy and Mutual Information
Abstract
This paper explores some applications of a two-moment inequality for the integral of the -th power of a function, where . The first contribution is an upper bound on the R\'{e}nyi 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.
Keywords
Cite
@article{arxiv.1702.07302,
title = {Two-Moment Inequalities for R\'enyi Entropy and Mutual Information},
author = {Galen Reeves},
journal= {arXiv preprint arXiv:1702.07302},
year = {2017}
}