Relative entropy via non-sequential recursive pair substitutions

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.

13 pages , 2 figures

References in corpus (3)

• Language Trees and Zipping
• Data compression and learning in time sequences analysis
• Non Sequential Recursive Pair Substitution: Some Rigorous Results