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

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Time Series Analysis

Background:

• Inferring nonlinear causal directional relations from observational time-series data is a key challenge in understanding complex systems.
• Estimating causal relationships in large systems with limited temporal observations remains an unresolved problem.

Purpose of the Study:

• Introduce large-scale nonlinear Granger causality (lsNGC) to facilitate conditional Granger causality estimation.
• Enable causal inference between multivariate time series, conditioned on numerous confounding series with minimal data.
• Address the challenge of identifying causal relations in large-scale systems with short time-series recordings.

Main Methods:

• lsNGC models interactions using nonlinear state-space transformations from limited observational data.
• It identifies causal relations without a priori assumptions on functional interdependence.
• The method offers a mathematical formulation for statistical significance of inferred causal relations.

Main Results:

• lsNGC successfully infers directed relations in chaotic time-series systems ranging from two to thirty-four nodes.
• The method captures meaningful interactions from limited data, outperforming traditional approaches.
• It demonstrates applicability to real-world systems, including functional Magnetic Resonance Imaging (fMRI) data.

Conclusions:

• lsNGC is an efficient and effective method for inferring nonlinear causal relationships from limited observational time-series data.
• The approach is suitable for large-scale systems and provides statistical significance for inferred relations.
• lsNGC shows promise for analyzing complex biological systems like the human brain using fMRI data.