Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 641-654 |
| Number of pages | 14 |
| Journal | Canadian Mathematical Bulletin |
| Volume | 60 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2017 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Canadian Mathematical Society 2016.
Keywords
- Alexandrov-Fenchel inequality
- F-dissimilarity
- F-divergence
- Isoperimetric inequality