Sharp Inequalities for $f$-divergences
Abstract
-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an -divergence between two probability measures subject to a finite number of constraints on other -divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between -divergences. We demonstrate that many of the existing results on inequalities between -divergences can be obtained as special cases of our results and we also improve on some existing non-sharp inequalities.
Cite
@article{arxiv.1302.0336,
title = {Sharp Inequalities for $f$-divergences},
author = {Adityanand Guntuboyina and Sujayam Saha and Geoffrey Schiebinger},
journal= {arXiv preprint arXiv:1302.0336},
year = {2013}
}