2014/01/28 by Umut Caglar, Caglar, Umut, Elisabeth M. Werner +1 · 2 citations
Decision Sciences · Mathematics · #Affine transformation #Combinatorics #Computer science #Concave function #Divergence (linguistics) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry #Inequality #Invariant (physics) #Isoperimetric inequality #Mathematical Inequalities and Applications #Mathematical analysis #Mathematical physics #Mathematics #Measure (data warehouse) #Multi-Criteria Decision Making #Point processes and geometric inequalities #Pure mathematics #Regular polygon #math.FA
paper · pdf · doi:10.48550/arxiv.1401.7065
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2014/01/28 · arxiv created 2016/06/27 · arxiv updated 2016/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Lλ-affine surface areas for log concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santaló type inequality.