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

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