In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time series data. In Sinha and Vaidya (in: IEEE conference on decision and control, pp 7329–7334, 2016), we have shown that the existing measures of information transfer, namely directed information, Granger causality and transfer entropy, fail to capture the causal interaction in a dynamical system and proposed a new definition of information transfer that captures direct causal interactions. The novelty of the information transfer definition used in this paper is the fact that it can differentiate between direct and indirect influences Sinha and Vaidya (2016). The main contribution of this paper is to show that the proposed definition of information transfers in Sinha and Vaidya (2016) and Sinha and Vaidya (in: Indian control conference, pp 303–308, 2017) can be computed from time series data, and thus, the direct influences in a dynamical system can be identified from time series data. We use transfer operator theoretic framework, involving Perron–Frobenius and Koopman operators for the data-driven approximation of the system dynamics and computation of information transfer. Several examples, involving linear and nonlinear system dynamics, are presented to verify the efficiency of the developed algorithm.

中文翻译：

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离散动力系统中因果推理的信息传递数据驱动计算

在本文中，我们提供了一种从时间序列数据中捕获动力系统中因果关系的新颖方法。在Sinha和Vaidya（2016年IEEE决策与控制会议，第7329–7334页）中，我们表明，现有的信息传递度量（即有向信息，格兰杰因果关系和传递熵）无法捕获因果关系。一个动态系统，并提出了一种新的信息传递定义，它可以捕获直接的因果关系。本文使用的信息传输定义的新颖之处在于，它可以区分直接影响和间接影响Sinha和Vaidya（2016）。本文的主要贡献在于表明Sinha和Vaidya（2016）以及Sinha和Vaidya（在印度控制会议上，（第303-308页，2017年）可以从时间序列数据中计算出来，因此，可以从时间序列数据中识别出动态系统中的直接影响。我们使用涉及Perron–Frobenius和Koopman算子的转移算子理论框架，对系统动力学进行数据驱动的近似并计算信息转移。提出了一些涉及线性和非线性系统动力学的示例，以验证所开发算法的效率。