On the mixed $f$-divergence for multiple pairs of measures
Information Theory
2013-04-26 v1 math.IT
Metric Geometry
Abstract
In this paper, the concept of the classical -divergence (for a pair of measures) is extended to the mixed -divergence (for multiple pairs of measures). The mixed -divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed -divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric type inequality for the mixed -divergence will be proved and applications in the theory of convex bodies are given.
Keywords
Cite
@article{arxiv.1304.6792,
title = {On the mixed $f$-divergence for multiple pairs of measures},
author = {Elisabeth M. Werner and Deping Ye},
journal= {arXiv preprint arXiv:1304.6792},
year = {2013}
}