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 $\mathcal{E}$.
Citation
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
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