Tight Lower Bounds for $\alpha$-Divergences Under Moment Constraints and Relations Between Different $\alpha$

arXiv2105.12972MaRDI QIDQ6368672

Author name not available (Why is that?)

Publication date: 27 May 2021

Abstract: The $alpha$-divergences include the well-known Kullback-Leibler divergence, Hellinger distance and $ch{i}^2$-divergence. In this paper, we derive differential and integral relations between the $alpha$-divergences that are generalizations of the relation between the Kullback-Leibler divergence and the $ch{i}^2$-divergence. We also show tight lower bounds for the $alpha$-divergences under given means and variances. In particular, we show a necessary and sufficient condition such that the binary divergences, which are divergences between probability measures on the same $2$-point set, always attain lower bounds. Kullback-Leibler divergence, Hellinger distance, and $ch{i}^2$-divergence satisfy this condition.

Has companion code repository: https://github.com/nissy220/TotalVariationDistance

This page was built for publication: Tight Lower Bounds for $\alpha$-Divergences Under Moment Constraints and Relations Between Different $\alpha$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6368672)