An information-geometric approach to a theory of pragmatic structuring

Abstract

Within the framework of information geometry, the interaction among units of a stochastic system is quantified in terms of the KullbackLeibler 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 ε are studied. In the corresponding dynamical setting, such points can be generated by the structuring process with respect to ε as a repelling set. The main results concern the low complexity of such distributions which can be controlled by the dimension of ε.