Canadian Mathematical Society
Canadian Mathematical Society
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Mixed $f$-divergence for Multiple Pairs of Measures

 Printed: Sep 2017
  • Elisabeth Werner
  • Deping Ye
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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.
Keywords: Alexandrov-Fenchel inequality, $f$-dissimilarity, $f$-divergence, isoperimetric inequality Alexandrov-Fenchel inequality, $f$-dissimilarity, $f$-divergence, isoperimetric inequality
MSC Classifications: 28-XX, 52-XX, 60-XX show english descriptions unknown classification 28-XX
unknown classification 52-XX
unknown classification 60-XX
28-XX - unknown classification 28-XX
52-XX - unknown classification 52-XX
60-XX - unknown classification 60-XX

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