Geometry of information structures, strategic measures and associated stochastic control topologies

On Information Structures and Nonsequential Stochastic Control

In many of the present controlled large-scale systems-communication and computer networks, detection networks, manufacturing systems, economic systems, database systems, power systems, etc.-information is decentralized. Furthermore , in the abovementioned systems it may be impossible to order the control actions a priori, independently of the set of control laws that determines these actions. S...

Strategic Measures in Optimal Control Problems for Stochastic Sequences

Controlled discrete-time stochastic processes are studied using the convex-analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.

Information geometry on complexity and stochastic interaction

Stochastic Reasoning, Free Energy, and Information Geometry

Belief propagation (BP) is a universal method of stochastic reasoning. It gives exact inference for stochastic models with tree interactions and works surprisingly well even if the models have loopy interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. This article gives a unified framework for u...

Information Geometry on Complexity and Stochastic Interaction

Interdependencies of stochastically interacting units are usually quantified by the Kullback-Leibler divergence of a stationary joint probability distribution on the set of all configurations from the corresponding factorized distribution. This is a spatial approach which does not describe the intrinsically temporal aspects of interaction. In the present paper, the setting is extended to a dyna...