Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
Department of Mechanical and Aerospace Engineering and Department of Biomedical Engineering, New York University Tandon School of Engineering, 6 MetroTech Center, Brooklyn, New York 11201, USA.
Chaos. 2020 Feb;30(2):023125. doi: 10.1063/1.5115510.
Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.
传递熵是一种可行的无模型工具，可以从时间序列推断两个动力系统之间的因果关系。从信息论的角度来看，传递熵将因果关系与有向信息传递联系起来，使得人们可以从另一个系统的历史中提高对动力系统未来的预测。最近的研究提出了使用传递熵来重建网络，但该度量的固有二元性质挑战了开发一种稳健方法的能力，这种方法可以区分节点之间的直接和间接相互作用。在本文中，我们通过在传递熵计算中引人时间延迟，试图弥补这一方法上的差距。通过认识到网络中的信息传递受到有限速度的限制，我们将两个节点之间的时滞传递熵的值与它们之间的游走次数联系起来。在此前提下，我们为网络重建提出了一个替代框架的基础，并通过对三节点网络的闭式结果和对使用布尔模型和混沌映射的更大网络的数值验证来说明这一点。
