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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2011Embargo end date: 01 Jul 2010Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Information Theory, volume 57, pages 3,230-3,235 (issn: 0018-9448, eissn: 1557-9654, Copyright policy )
Authors: Peter Harremoës; Igor Vajda;

doi: 10.1109/tit.2011.2137353 , 10.48550/arxiv.1007.0097

arXiv: 1007.0097

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

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. Some applications of this result are given.

7 pages, 4 figures

Keywords

FOS: Computer and information sciences, 94A17, 26Dxx, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Mathematics, Mathematics - Statistics Theory, Statistics Theory (math.ST)

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 25
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
25
Top 10%
Top 10%
Average
Green
bronze