Geodesic
Mixed ƒ-divergence for Multiple Pairs of Measures
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 641-654

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DOI

In this paper, the concept of the classical $f$ -divergence for a pair of measures is extended to the mixed $f$ -divergence formultiple pairs ofmeasures. 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.
DOI : 10.4153/CMB-2016-050-3
Mots-clés : 28-XX, 52-XX, 60-XX, Alexandrov–Fenchel inequality, ƒ-dissimilarity, ƒ-divergence, isoperimetric inequality 
Werner, Elisabeth; Ye, Deping. Mixed ƒ-divergence for Multiple Pairs of Measures. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 641-654. doi: 10.4153/CMB-2016-050-3
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     author = {Werner, Elisabeth and Ye, Deping},
     title = {Mixed {\textflorin}-divergence for {Multiple} {Pairs} of {Measures}},
     journal = {Canadian mathematical bulletin},
     pages = {641--654},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2016-050-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-050-3/}
}
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