Causal coupling inference from multivariate time series based on ordinal partition transition networks

Narayan Puthanmadam Subramaniyam,Reik V Donner,Gabriella Panuccio,Jari Hyttinen,Davide Caron

doi:10.1007/s11071-021-06610-0

Abstract

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.

Highlights

The detection of causal interactions is a fundamental problem in both natural and social sciences [1,2]
To overcome the aforementioned limitations of previous ordinal partition transition networks (OPTNs)-based methods, in this work we propose an extension of OPTN-based time series analysis, which leverages the construction of multiple bipartite OPTNs (M-OPTN) to account for multivariate time series
The results from the application of our method are shown in Fig. 16, where the plots on the main diagonal show the microelectrode array (MEA) signals acquired from the six selected regions of interest (ROIs)

Summary

Introduction

The detection of causal interactions is a fundamental problem in both natural and social sciences [1,2]. Since the classical Granger causality analysis is model-based and (in a strict sense) only valid for linear systems, more general bivariate approaches based on information theory have been proposed for identifying causality in applications to nonlinear dynamical systems [6]. These methods include, among others, transfer entropy [7], time-delayed mutual information [8], and the multivariate extension of transfer entropy [6]. Transfer entropy can be considered as a generalization of Granger causality for nonlinear systems [9], while it has been shown to be equivalent to Granger causality for linear Gaussian models [10]

Methods

Results

Discussion

Conclusion