Parameter scalability of multivariate Granger causality

Estimating causal interactions between signals provides unique insights into their dynamics. In neuroscience, causal inference has been widely used in electrophysio-logical data to shed light on brain communication. Multivariate autoregressive models (MVAR) often form the basis of causal estimation methods. However, given the high-dimensionality of whole-brain data, MVARs can become too large for proper estimation, and reducing the dimensions to a reasonable range affects causal inference. In this study, we provide a clear, practical range for each parameter, motivate the choice of the causal estimation algorithm, and guide the optimization of model parameters for practical analyses. To that end, we simulate electrophysiological data with underlying causalities and estimate the causality with current algorithms based on MVAR models. We then model how the samples, signals, and MVAR order affect the performance and computation time of each algorithm. Our results indicate that, although all algorithms scale at least quadratically with the three parameters together, some are more sensitive to the number of signals and others to the number of samples. We further reveal that the number of samples required for accurate causal inference depends on the number of signals involved. Generally, more recent algorithms designed for robustness scale worse in computation time than older, simpler algorithms. Overall, this work highlights the need to consider scalability in Granger causality inference.