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arXiv · 1606.08504

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 inequality for the mixed $f$-divergence are proved.

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Elisabeth M. Werner, Deping Ye. 2016-06-27. Mixed $f$-divergence for multiple pairs of measures. https://arxiv.org/abs/1606.08504

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