On the mixed f-divergence for multiple pairs of measures

2013/04/25 by Werner, Elisabeth M., Ye, Deping
#94A15 #94A17 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1304.6792

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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