Scaled Bregman divergences in a Tsallis scenario

R.C. Venkatesan and A. Plastino

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 15, 2749-2758

Abstract: There exist two different versions of the Kullback–Leibler divergence (K–Ld) in Tsallis statistics, namely the usual generalized K–Ld and the generalized Bregman K–Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized K–Ld forms is derived by recourse to the additive duality of Tsallis statistics. It is also shown that the usual generalized K–Ld subjected to this additive duality, known as the dual generalized K–Ld, is a scaled Bregman divergence. This leads to an interesting conclusion: the dual generalized mutual information is a scaled Bregman information. The utility and implications of these results are discussed.

Keywords: Generalized Tsallis statistics; Additive duality; Kullback–Leibler divergence; Scaled Bregman divergences; Scaled Bregman information (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437111002032
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:15:p:2749-2758

DOI: 10.1016/j.physa.2011.03.012

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().