Scaled Bregman divergences in a Tsallis scenario |
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Authors: | R.C. Venkatesan A. Plastino |
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Affiliation: | a Systems Research Corporation, Aundh, Pune 411007, Indiab IFLP, National University La Plata & National Research Council (CONICET), C. C., 727 1900, La Plata, Argentina |
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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. |
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Keywords: | Generalized Tsallis statistics Additive duality Kullback-Leibler divergence Scaled Bregman divergences Scaled Bregman information |
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