{
  "id": "1606.08504",
  "version": "v1",
  "published": "2016-06-27T22:38:46.000Z",
  "updated": "2016-06-27T22:38:46.000Z",
  "title": "Mixed $f$-divergence for multiple pairs of measures",
  "authors": [
    "Elisabeth M. Werner",
    "Deping Ye"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1304.6792",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T22:38:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple pairs",
      "divergence",
      "alexandrov-fenchel type inequality",
      "isoperimetric inequality",
      "permutation invariance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}