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arXiv · 1007.3384

Relative entropy via non-sequential recursive pair substitutions

D. Benedetto·E. Caglioti·G. Cristadoro·M. Degli Esposti
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Abstract

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way.

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D. Benedetto, E. Caglioti, G. Cristadoro, M. Degli Esposti. 2010-08-22. Relative entropy via non-sequential recursive pair substitutions. https://doi.org/10.1088/1742-5468%2F2010%2F09%2Fp09010

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