Parameter scaling of multivariate Granger causality

Estimating causal interactions between signals provides unique insights into their dynamics, and causal inference has been widely applied to electrophysiological data to elucidate brain communication. Multivariate autoregressive models (MVAR) form the basis of most causal estimation methods. However, the high dimensionality of whole-brain data renders MVARs difficult to estimate reliably, and reducing the dimensions to a reasonable range affects causal inference. To address these scalability limitations, we develop sparse Multivariate Granger Causality (sMVGC), a novel method premised on the assumption that true causal connections between signals are sparse, thereby constraining the candidate search space and improving scalability. To motivate sMVGC empirically, we simulate electrophysiological data with known causalities and model how the number of samples, signals, and MVAR order affect the performance and computation time of current algorithms. All algorithms scale at least quadratically with these parameters, yet differ in their sensitivity to signal versus sample count, and the sample requirements for accurate inference scale with the number of signals. Guided by these findings, sMVGC improves parameter scalability while preserving estimation accuracy, and we provide practical parameter ranges and model selection guidance for real-world analyses.