Correlation-induced suppression of Granger causality and Gaussian transfer entropy
Abstract
In complex dynamical systems, Granger causality and transfer entropy are widely used to infer directional interactions, but they quantify a source's unique predictive contribution after conditioning and can therefore be substantially attenuated by correlation with the retained variables. Here, using our previously developed Linear Operator Causality Analysis (LOCA) framework, which measures causal response from the system propagator, we derive a relationship between predictive and operator-based causality. For a two-dimensional linear system, the fractional suppression of Granger causality equals the squared correlation between source and receiver. We generalize this result to high-dimensional systems using the source covariance remaining after conditioning and show that additional conditioning can only increase the suppression. The same covariance ordering yields a corresponding upper bound for Gaussian transfer entropy. A linearized Burgers advection chain exhibits 36.6% suppression at the convective travel-time peak, and exact nonlinear acoustic Burgers solutions show that the fitted-surrogate penalty is governed by correlation structure rather than nonlinearity and remains robust to sensor noise after operator debiasing. Applied to resting-state fMRI from the Human Connectome Project (80 brain regions, 8 functional networks, 10 subjects), the single-lag Granger causality measure falls 39.4% below the operator response when conditioning only on the receiver and 73.0% when conditioning on the receiver and all other retained variables. The framework provides a quantitative bridge between predictive and operator-based causal measures in high-dimensional dynamical systems.
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BibTeX
@misc{cattafesta2026correlationinduced,
title = {{Correlation-induced suppression of Granger causality and Gaussian transfer entropy}},
author = {Louis Cattafesta and Scott T. M. Dawson and Ankit Srivastava},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32867},
eprint = {2610.32867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32867},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Correlation-induced suppression of Granger causality and Gaussian transfer entropy
AU - Louis Cattafesta
AU - Scott T. M. Dawson
AU - Ankit Srivastava
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32867
UR - https://arxiv.org/abs/2610.32867
AB - In complex dynamical systems, Granger causality and transfer entropy are widely used to infer directional interactions, but they quantify a source's unique predictive contribution after conditioning and can therefore be substantially attenuated by correlation with the retained variables. Here, using our previously developed Linear Operator Causality Analysis (LOCA) framework, which measures causal response from the system propagator, we derive a relationship between predictive and operator-based causality. For a two-dimensional linear system, the fractional suppression of Granger causality equals the squared correlation between source and receiver. We generalize this result to high-dimensional systems using the source covariance remaining after conditioning and show that additional conditioning can only increase the suppression. The same covariance ordering yields a corresponding upper bound for Gaussian transfer entropy. A linearized Burgers advection chain exhibits 36.6% suppression at the convective travel-time peak, and exact nonlinear acoustic Burgers solutions show that the fitted-surrogate penalty is governed by correlation structure rather than nonlinearity and remains robust to sensor noise after operator debiasing. Applied to resting-state fMRI from the Human Connectome Project (80 brain regions, 8 functional networks, 10 subjects), the single-lag Granger causality measure falls 39.4% below the operator response when conditioning only on the receiver and 73.0% when conditioning on the receiver and all other retained variables. The framework provides a quantitative bridge between predictive and operator-based causal measures in high-dimensional dynamical systems.
ER -