Echo-State networks for estimating directed functional connectivity.

Granger Causality estimation through multivariate vector autoregressive models suffers from strong limitations in nonlinear systems. We present a novel, versatile and widely applicable approach to estimating Granger Causality based on a specific class of recursive neural networks (RNN) termed echo-state networks (ESN). Using complex networks of non linear oscillators, we show that our approach provides discrimination performances which largely exceed the current state of the art. We then explore the structure of causal networks in the human brain employing functional MRI data from 1003 healthy subjects scanned at rest at 3 T within the human connectome project (HCP), demonstrating the existence of previously unknown directed within-brain interactions.