The entropy of an ergodic source is the limit of properly rescaled oneblock entropies of sources obtained applying successive non-sequential recursive pair substitutions (NSRPS). In this paper we prove that the cross-entropy and the Kullback–Leibler divergence can be obtained in a similar way.
Benedetto, D., Caglioti, E., Cristadoro, G., Degli Esposti, M. (2010). Relative entropy via non-sequential recursive pair substitution. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2010(9), 1-14 [10.1088/1742-5468/2010/09/P09010].
Relative entropy via non-sequential recursive pair substitution
Cristadoro, G;
2010
Abstract
The entropy of an ergodic source is the limit of properly rescaled oneblock entropies of sources obtained applying successive non-sequential recursive pair substitutions (NSRPS). 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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