On the mixed $f$-divergence for multiple pairs of measures

Elisabeth M. Werner; Deping Ye

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arXiv · 1304.6792

On the mixed $f$-divergence for multiple pairs of measures

Elisabeth M. Werner·Deping Ye

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Abstract

In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric type inequality for the mixed $f$-divergence will be proved and applications in the theory of convex bodies are given.

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Elisabeth M. Werner, Deping Ye. 2013-04-25. On the mixed $f$-divergence for multiple pairs of measures. https://arxiv.org/abs/1304.6792

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