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

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.

Biohybrid restoration of the hippocampal loop re-establishes the non-seizing state in an in vitro model of limbic seizures

“…Namely, we used Granger causality (GC) [59] and ordinal partition transition networks (OPTN) [50, 51] as two methods of causality inference based on different mathematical principles: while GC measures are valid only for linear interactions, OPTN-based causality measures are sensitive to both linear and nonlinear ones; hence, their combination provides complementary information about statistically inferred coupling. As shown Figure 2D , the GC values demonstrated that the bridge increased the causal relationship between CA3 and CTX in the two directions of the loop (CA3-to-CTX – CTRL1: 0.05 ± 0.01; bridge: 0.44 ± 0.06; CTRL2: 0.05 ± 0.02; one-way ANOVA, F(df): 44.47(2), p < 0.001 bridge vs both CTRLs.…”

“…Taken's embedding theorem [52] was used to reconstruct the phase space and obtain the ordinal patterns. For phase space reconstruction, the embedding delay was chosen based on auto mutual-information [53], whereas the embedding dimension was set to 3 based on the data length (200000 samples/window) [51,53,54]. For each time window, the causality was tested for delays ranging from 1 to 100 ms in 1-ms steps.…”

“…The first method, Granger causality (GC), is an established approach to quantify how well one time series can be predicted from another [46]; it explores the system as a linear regression of a stochastic process to measure the amount of information transferred between two signals and yields unique characteristics of signal B inside signal A. The second method is based on ordinal partition transition networks (OPTNs); this is a relatively new approach to infer the coupling and its direction between two dynamical systems [50], which was recently extended to detect causality in multivariate observational data, such as MEA recordings, by removing non-causal nodes at various interaction delays [51].…”

“…Thus, for a pair of signals we obtained time-varying OPTN-based causality measure in the form of a N x N x W matrix, where N = 2 and W = n windows; in this matrix, the off-diagonal entries represent the causal interaction among the signals, whereas the diagonal entries represent self-connections and are ignored. Comparison of the causal strength across protocols relied on the empirical cumulative distribution function (CDF) of the OPTN-derived causality normalized to a range of 0 to 1 [51].…”

Assessing causal dependencies in climatic indices

“…Many approaches for causal inference have been proposed in the literature, based of model reconstruction, information theory, phase-space reconstruction, nonlinear symbolic analysis, machine learning, etc. (Granger 1969;Schreiber 2000;Baccala and Sameshima 2001;Eichler et al 2003;Sugihara 2012;Runge 2018;Siyang Leng et al 2020;Subramaniyam et al 2021;Huang et al 2020). These approaches have different mathematical hypotheses and computational complexity, and they differ considerably in their capability to detect genuine couplings (Krakovska et al 2018).…”