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Assessing Coupling Dynamics from an Ensemble of Time Series

机译：从时间序列集合中评估耦合动力学

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Finding interdependency relations between time series provides valuable knowledge about the processes that generated the signals. Information theory sets a natural framework for important classes of statistical dependencies. However, a reliable estimation from information-theoretic functionals is hampered when the dependency to be assessed is brief or evolves in time. Here, we show that these limitations can be partly alleviated when we have access to an ensemble of independent repetitions of the time series. In particular, we gear a data-efficient estimator of probability densities to make use of the full structure of trial-based measures. By doing so, we can obtain time-resolved estimates for a family of entropy combinations (including mutual information, transfer entropy and their conditional counterparts), which are more accurate than the simple average of individual estimates over trials. We show with simulated and real data generated by coupled electronic circuits that the proposed approach allows one to recover the time-resolved dynamics of the coupling between different subsystems.
机译：查找时间序列之间的相互依赖关系可以提供有关生成信号的过程的有价值的知识。信息论为重要的统计依存关系类别设置了自然的框架。但是，当要评估的依存关系短暂或随时间演变时，会妨碍从信息理论功能进行可靠的估计。在这里，我们表明，当我们可以访问时间序列的独立重复集合时，可以部分缓解这些限制。特别是，我们采用概率密度的数据有效估计器，以利用基于试验的度量的完整结构。这样，我们可以获得一系列熵组合（包括互信息，传递熵及其有条件的对等物）的时间分辨估计，该估计比试验中单个估计的简单平均值更为准确。我们通过耦合电子电路生成的模拟和真实数据表明，该方法可以恢复不同子系统之间耦合的时间分辨动力学。

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