Entropy Concentration and the Empirical Coding Game (0809.1017v1)

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, areclose' 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.