An Information-Geometric Approach to a Theory of Pragmatic Structuring

Ay, Nihat

Ann. Probab., Tome 30 (2002) no. 1, p. 416-436 / Harvested from Project Euclid

Résumé

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 $\mathcal{E}$.

Détail

Publié le : 2002-01-14
Classification:  Information geometry,  Kullback-Leibler divergence,  mutual information,  infomax principle,  stochastic interaction,  exponential family,  62H20,  92B20,  62B05,  53B05