We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
55/2015
The Information Bottleneck Method for Optimal Prediction of Multilevel Agent-based Systems
Robin Lamarche-Perrin, Sven Banisch and Eckehard Olbrich
Abstract
Because the dynamics of complex systems is the result of both decisive local events and reinforced global effects, the prediction of such systems could not do without a genuine multilevel approach. This paper proposes to found such an approach on information theory. Starting from a complete microscopic description of the system dynamics, we are looking for observables of the current state that allows to efficiently predict future observables. Using the framework of the Information Bottleneck method, we relate optimality to two aspects: the complexity and the predictive capacity of the retained measurement. Then, with a focus on Agent-based Models, we analyse the solution space of the resulting optimisation problem in a generic fashion. We show that, when dealing with a class of feasible measurements that are consistent with the agent structure, this solution space has interesting algebraic properties that can be exploited to efficiently solve the problem. We then present results of this general framework for the Voter Model with several topologies and show that, especially when predicting the state of some sub-part of the system, multilevel measurements turn out to be the optimal predictors.
