Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

Axel Wismüller,Adora M Dsouza,M Ali Vosoughi,Anas Abidin

doi:10.1038/s41598-021-87316-6

Axel Wismüller, Adora M Dsouza + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-87316-6

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Abstract

A key challenge to gaining insight into complex systems is inferring nonlinear causal directional relations from observational time-series data. Specifically, estimating causal relationships between interacting components in large systems with only short recordings over few temporal observations remains an important, yet unresolved problem. Here, we introduce large-scale nonlinear Granger causality (lsNGC) which facilitates conditional Granger causality between two multivariate time series conditioned on a large number of confounding time series with a small number of observations. By modeling interactions with nonlinear state-space transformations from limited observational data, lsNGC identifies casual relations with no explicit a priori assumptions on functional interdependence between component time series in a computationally efficient manner. Additionally, our method provides a mathematical formulation revealing statistical significance of inferred causal relations. We extensively study the ability of lsNGC in inferring directed relations from two-node to thirty-four node chaotic time-series systems. Our results suggest that lsNGC captures meaningful interactions from limited observational data, where it performs favorably when compared to traditionally used methods. Finally, we demonstrate the applicability of lsNGC to estimating causality in large, real-world systems by inferring directional nonlinear, causal relationships among a large number of relatively short time series acquired from functional Magnetic Resonance Imaging (fMRI) data of the human brain.

Highlights

Identifying nonlinear and directed relations between components of a complex system, especially from simultaneously observed time series, is an actively growing area of r esearch[1,2,3,4,5]
Several benchmark simulations are considered and performance is compared to four state-of-the-art approaches, mutual nonlinear cross-mapping methods[15] using local models (LM), PC-momentary conditional independence (PCMCI)[18], multivariate transfer entropy (TE)[8] with the Kraskov-StögbauerGrassberger nonlinear estimators[22] using the IDTxL toolbox[27], and Kernel Granger Causality (KGC)[20]
These results demonstrate that KGC cannot capture right connections for a relatively large network with just few time-points

Summary

Introduction

Identifying nonlinear and directed relations between components of a complex system, especially from simultaneously observed time series, is an actively growing area of r esearch[1,2,3,4,5]. A causality analysis method should 1) be able to estimate causal interactions in multivariate systems, conditioned on all time series in the system, 2) be able to capture nonlinear dependencies, 3) work for systems with a large number of variables, and 4) be data-driven[18]. Nonlinear extensions of GC have been proposed in7, and kernelbased nonlinear GC approaches in[19,20,21], such approaches require a large number of observations to estimate causal relations effectively Possible reasons for these restrictions are: besides the computational expense, the extendibility to multivariate analysis of high-dimensional dynamical systems based on a low number of temporal observations is non-trivial and involves parameter optimization of complex nonlinear time-series models on limited data. If lsNGC measures can characterize brain connectivity well, it should be useful in distinguishing the two subject groups

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