On Pairs of $f$ -Divergences and Their Joint Range

  • Authors:

  • P. Harremoes;I. Vajda

  • Affiliations:

  • Copenhagen Bus. Coll., Copenhagen, Denmark;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2011

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Abstract

We compare two f-divergences and prove that their joint range is the convex hull of the joint range for distributions supported on only two points. The proofs use various methods from topology and convex analysis.