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

09/14/2019

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by   V. I. Bakhtin, et al.

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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.