A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations.

Area of Science:

• Neuroscience
• Computational Neuroscience
• Systems Neuroscience

Background:

• High-frequency neuroelectric signals (EEG, MEG) offer insights into brain area causal relationships.
• Classical Granger causality (GC) faces limitations with high-dimensional, densely connected brain data and long-range dependencies.
• Existing methods often require high model orders, complicating parameter estimation.

Purpose of the Study:

• To generalize autoregressive models for improved Granger causality (GC) estimation.
• To develop a method capable of capturing long-range dependencies in brain signals without increasing model complexity.
• To enhance the analysis of directed brain connectivity using neuroimaging data.

Main Methods:

• Utilized Wiener-Volterra decompositions with Laguerre polynomials as basis functions to generalize autoregressive models.
• Introduced a single global parameter to capture long-range dependencies, maintaining model simplicity and linearity.
• Validated the method using synthetic data from complex networks and real MEG data from the Human Connectome Project (HCP).

Main Results:

• The proposed method demonstrated superior performance compared to classical Granger causality on synthetic data.
• The framework successfully captured long-range dependencies without increasing model order.
• Analysis of Human Connectome Project (HCP) MEG data revealed known and novel directed influences between cortical and limbic regions.

Conclusions:

• The generalized autoregressive model offers a simplified, linear, and easily estimable approach for causal inference in high-dimensional neuroimaging data.
• This method advances the study of the directed human brain connectome, improving upon classical Granger causality.
• The framework has the potential to uncover complex causal interactions within the brain, contributing to a deeper understanding of brain function.