Mixed $f$-divergence for Multiple Pairs of Measures
Printed: Sep 2017
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.
Alexandrov-Fenchel type inequality and an isoperimetric inequality
mixed $f$-divergence are proved.
Alexandrov-Fenchel inequality, $f$-dissimilarity, $f$-divergence, isoperimetric inequality
28-XX - unknown classification 28-XX
52-XX - unknown classification 52-XX
60-XX - unknown classification 60-XX