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.
Bibliographical noteFunding Information:
Partially supported by an NSF grant. Supported by an NSERC grant and a start-up grant from Memorial University of Newfoundland.
© Canadian Mathematical Society 2016.
- Alexandrov-Fenchel inequality
- Isoperimetric inequality