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January 2002 An Information-Geometric Approach to a Theory of Pragmatic Structuring
Nihat Ay
Ann. Probab. 30(1): 416-436 (January 2002). DOI: 10.1214/aop/1020107773

Abstract

Within the framework of information geometry, the interaction among units of a stochastic system is quantified in terms of the Kullback–Leibler divergence of the underlying joint probability distribution from an appropriate exponential family. In the present paper, the main example for such a family is given by the set of all factorizable random fields. Motivated by this example, the locally farthest points from an arbitrary exponential family $\mathcal{E}$ are studied. In the corresponding dynamical setting, such points can be generated by the structuring process with respect to $\mathcal{E}$ as a repelling set. The main results concern the low complexity of such distributions which can be controlled by the dimension of $\mathcal{E}$.

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Nihat Ay. "An Information-Geometric Approach to a Theory of Pragmatic Structuring." Ann. Probab. 30 (1) 416 - 436, January 2002. https://doi.org/10.1214/aop/1020107773

Information

Published: January 2002
First available in Project Euclid: 29 April 2002

zbMATH: 1010.62007
Digital Object Identifier: 10.1214/aop/1020107773

Subjects:
Primary: 53B05 , 62B05 , 62H20 , 92B20

Keywords: exponential family , infomax principle , information geometry , Kullback-Leibler divergence , mutual information , stochastic interaction

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 1 • January 2002
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