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The Information Bottleneck Method For Optimal Prediction Of Multilevel Agent-Based Systems

Author

Listed:
  • ROBIN LAMARCHE-PERRIN

    (Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany)

  • SVEN BANISCH

    (Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany)

  • ECKEHARD OLBRICH

    (Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany)

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 (IB) 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 (ABMs), we analyze the solution space of the resulting optimization 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 (VM) 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.

Suggested Citation

  • Robin Lamarche-Perrin & Sven Banisch & Eckehard Olbrich, 2016. "The Information Bottleneck Method For Optimal Prediction Of Multilevel Agent-Based Systems," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-45, February.
    • Handle: RePEc:wsi:acsxxx:v:19:y:2016:i:01n02:n:s0219525916500028
    DOI: 10.1142/S0219525916500028
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    References listed on IDEAS

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