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Sup-Sums Principles for F-Divergence and a New Definition for t-Entropy
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2020-11-04 , DOI: 10.1007/s10959-020-01046-5
V. I. Bakhtin 1, 2 , A. V. Lebedev 2, 3
Affiliation  

The article presents new \({\sup }\)-sums principles for integral F-divergence for arbitrary convex functions F on the whole real axis and arbitrary (not necessarily positive and normalized) measures. Among applications of these results, we work out a new ‘integral’ definition for t-entropy explicitly establishing its relation to Kullback–Leibler divergence.



中文翻译:

F-Divergence 的 Sup-Sums 原理和 t-Entropy 的新定义

这篇文章提出了新的\({\sup }\) -sums 积分F - 散度的原理,用于整个实轴上的任意凸函数F和任意(不一定是正的和归一化的)度量。在这些结果的应用中,我们为t熵制定了一个新的“积分”定义,明确地建立了它与 Kullback-Leibler 散度的关系。

更新日期:2020-11-04
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