Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data.

在流行病学、气候学、生态学、基因组学、经济学和神经科学等许多科学领域中，确定因果关系是一个具有挑战性但又至关重要的问题，仅举几例。最近的研究表明，序数分区转换网络 (OPTN) 允许推断两个动态系统之间的耦合方向。在这项工作中，我们将这一概念推广到研究多个动力系统之间的相互作用，并提出了一种新方法来检测多元观测数据中的因果关系。通过将此方法应用于耦合线性随机过程的数值模拟以及相互作用的非线性动力系统的两个示例（耦合洛伦兹系统和神经质量模型网络），我们证明了我们的方法可以可靠地识别交互方向和相关的耦合延迟。最后，我们研究了来自啮齿动物脑切片的真实观察微电极阵列电生理数据，以确定癫痫样活动背后的因果耦合结构。我们来自模拟和现实世界数据的结果表明，OPTN 可以提供一种互补且稳健的方法来从多变量观察数据中推断因果效应网络。