Identifying causal relationships is a challenging yet a 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 to infer the coupling direction between two dynamical systems. In this work, we generalize this concept to the interaction between multiple dynamical systems and  propose a new method to detect causality in multivariate observational data. We demonstrate that our approach can reliably identify the direction of interaction and the corresponding delays with numerical simulations using linear stochastic systems as well as  nonlinear dynamical systems such as a network of neural mass models  . Finally, we apply our method to real-world observational microelectrode array  data from rodent brain slices to study the causal effect networks underlying epileptic activity. Our results from simulations as well as real-world data  suggest that OPTNs can provide a complementary approach to reliably infer causal effect networks from multivariate observational data.
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.
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