Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 14: Complex Systems
DY 14.3: Vortrag
Montag, 7. März 2016, 16:45–17:00, H47
Scale dependent complexity measure for time series — •Eckehard Olbrich1 and Georg Martius2 — 1Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany — 2IST Austria, Klosterneuburg, Austria
The predictive information - also known as effective measure complexity or excess entropy - is a natural complexity measure for temporal sequences. It measures the amount of information that the past contains about the future which is equal to the non-extensive part of the entropy of the sequence. In order to apply it to dynamical systems with continuous states one has to partition the state space first. But, then the result will depend on the partition and will be different even for different generating partitions. Here we will study the excess entropy using scale dependent entropies. We show that the excess entropy becomes infinite in the limit of infinite resolution for deterministic systems. The attractor dimension controls, how the excess entropy diverges with increasing resolution while the resolution independent offset provides a complexity measure on its own --- if appropriately rescaled --- that is related to the correlations. Moreover, we show that the excess entropy remains finite for noisy systems, and discuss how it is determined by the noise levels and the entropy rate on the large scales. We demonstrate the usefulness of the scale dependent excess entropy using it for quantifying the effects of autonomously learned behavior of simulated robots using task independent objective functions.
G. Martius and E. Olbrich, Quantifying Emergent Behavior of Autonomous Robots, Entropy 17(10), 2015, 7266-7297.