Mixed f-divergence and inequalities for log concave functions

2014/01/28 by Umut Caglar, Caglar, Umut, Elisabeth M. Werner +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Multi-Criteria Decision Making #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1401.7065

openalex publication_date 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mixed f-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions. Special cases of f-divergences are mixed L_λ-affine surface areas for log concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santaló type inequality.

Citations

• Mixed f-divergence for multiple pairs of measures

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