Nonextensive Generalizations of the Jensen-Shannon Divergence

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Convexity is a key concept in information theory, namely via the many implications of Jensen's inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen's inequality also underlies the concept of Jensen-Shannon divergence (JSD), which is a symmetrized and smoothed version of the KLD. This paper introduces new JSD-type divergences, by extending its two building blocks: convexity and Shannon's entropy. In particular, a new concept of q-convexity is introduced and shown to satisfy a Jensen's q-inequality. Based on this Jensen's q-inequality, the Jensen-Tsallis q-difference is built, which is a nonextensive generalization of the JSD, based on Tsallis entropies. Finally, the Jensen-Tsallis q-difference is charaterized in terms of convexity and extrema.
Submitted to the IEEE Transactions on Information Theory

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Information Theory, Statistics Theory, 94A17; 94A15

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http://salesiana.dossiersoluciones.com/handle/123456789/158490

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.1653
 http://arxiv.org/abs/0804.1653

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arXiv