Deformed Statistics Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework

R. C. Venkatesan; A. Plastino

doi:10.1016/j.physleta.2011.09.021

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arXiv · 1102.1025

Deformed Statistics Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework

R. C. Venkatesan·A. Plastino

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Abstract

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information-principle using the dual generalized K-Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K-Ld, with normal averages constraints, is shown to exhibit distinctly unique features.

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cond-mat.stat-mech cs.IT math-ph math.IT math.MP

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BibTeX RIS

R. C. Venkatesan, A. Plastino. 2011-02-04. Deformed Statistics Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework. https://doi.org/10.1016/j.physleta.2011.09.021

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