Mixed f-divergence for multiple pairs of measures

2016/06/27 by Elisabeth M. Werner, Werner, Elisabeth M., Deping Ye +1
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1606.08504

openalex publication_date 2016/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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