Recurrent neural networks for reconstructing complex directed brain connectivity

While Granger Causality(GC)-based approaches have been widely employed in a vast number of problems in network science, the vast majority of GC applications are based on linear multivariate autoregressive (MVAR) models. However, it is well known that real-life system (and biological networks in particular) exhibit notable nonlinear behavior, hence undermining that validity of MVAR-based approaches to estimating GC (MVAR-GC). In this paper, we define a novel approach to estimating nonlinear, directed within-network interactions based on a specific class of recurrent neural networks (RNN) termed echo-state networks (ESN). We reformulate the classical GC framework in terms of ESN-based models for multivariate signals generated by arbitrarily complex networks, and characterize the ability of our ESN-based Granger Causality (ES-GC) to capture nonlinear causal relations by simulating multivariate coupling in a network of nonlinearly interacting, noisy Duffing oscillators operating in a chaotic regime. Synthetic validation shows a net advantage of ES-GC over all other estimators in detecting nonlinear, causal links. We then explore the structure of EC-GC networks in the human brain in functional MRI data from 1003 healthy subjects scanned at rest at 3T, discovering previously unknown between-network interactions. In summary, ES-GC performs significantly better than commonly used and recently developed GC detection tools, making it a superior tool for the analysis of e.g. multivariate biological networks.