Entropy Concentration and the Empirical Coding Game

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We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's `conditional limit theorem'. The theorems characterize exactly in what sense a prior distribution Q conditioned on a given constraint, and the distribution P, minimizing the relative entropy D(P ||Q) over all distributions satisfying the constraint, are `close' to each other. We then apply our theorems to establish the relationship between entropy concentration and a game-theoretic characterization of Maximum Entropy Inference due to Topsoe and others.
A somewhat modified version of this paper was published in Statistica Neerlandica 62(3), pages 374-392, 2008

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Information Theory, Machine Learning, Statistics Theory, Methodology

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http://salesiana.dossiersoluciones.com/handle/123456789/169193

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.1017
 http://arxiv.org/abs/0809.1017

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arXiv