The Annals of Probability

An Information-Geometric Approach to a Theory of Pragmatic Structuring

Nihat Ay

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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 $\mathcal{E}$.

Article information

Source
Ann. Probab., Volume 30, Number 1 (2002), 416-436.

Dates
First available in Project Euclid: 29 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1020107773

Digital Object Identifier
doi:10.1214/aop/1020107773

Mathematical Reviews number (MathSciNet)
MR1894113

Zentralblatt MATH identifier
1010.62007

Subjects
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.) 92B20: Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx] 62B05: Sufficient statistics and fields 53B05: Linear and affine connections

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

Citation

Ay, Nihat. An Information-Geometric Approach to a Theory of Pragmatic Structuring. Ann. Probab. 30 (2002), no. 1, 416--436. doi:10.1214/aop/1020107773. https://projecteuclid.org/euclid.aop/1020107773


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