Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropy

TL;DR

This paper introduces new sup-sums principles for F-divergence and Kullback-Leibler divergence, along with a novel integral definition for t-entropy, expanding theoretical understanding of these measures.

Contribution

It develops generalized sup-sums principles for integral F-divergence and proposes a new integral definition for t-entropy, linking it to Kullback-Leibler divergence.

Findings

Derived sup-sums principle for Kullback-Leibler divergence

Established a new integral definition for t-entropy

Connected t-entropy with Kullback-Leibler divergence

Abstract

The article presents new sup-sums principles for integral F-divergence for arbitrary convex function F and arbitrary (not necessarily positive and absolutely continuous) measures. As applications of these results we derive the corresponding sup-sums principle for Kullback--Leibler divergence and work out new `integral' definition for t-entropy explicitly establishing its relation to Kullback--Leibler divergence.