Orlicz addition for measures and an optimization problem for the $f$-divergence
Metric Geometry
2016-06-08 v1 Probability
Abstract
In this paper, the Orlicz addition of measures is proposed and an interpretation of the -divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional Orlicz-Brunn-Minkowski inequality, are established. We also investigate an optimization problem for the -divergence and establish functional affine isoperimetric inequalities for the dual functional Orlicz affine and geominimal surface areas of measures.
Keywords
Cite
@article{arxiv.1606.02155,
title = {Orlicz addition for measures and an optimization problem for the $f$-divergence},
author = {Shaoxiong Hou and Deping Ye},
journal= {arXiv preprint arXiv:1606.02155},
year = {2016}
}