Entropy Concentration and the Empirical Coding Game

Peter Grunwald

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arXiv · 0809.1017

Entropy Concentration and the Empirical Coding Game

Peter Grunwald

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Abstract

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.

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Peter Grunwald. 2008-09-05. Entropy Concentration and the Empirical Coding Game. https://arxiv.org/abs/0809.1017

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