Inferring directionality of coupled dynamical systems using Gaussian process priors: Application on neurovascular...

Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM). In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction. Furthermore, CCM's capacity to detect indirect causal links may be challenged in simulated unidrectionally coupled Rossler-Lorenz systems. To overcome these limitations, we propose a method that places a Gaussian process prior on a cross mapping function (named GP-CCM) to impose constraints on local state space neighborhood comparisons. Bayesian posterior likelihood and evidence ratio tests, as well as surrogate data analyses are performed to obtain a robust statistic for dynamical coupling directionality. We demonstrate GP-CCM's performance with respect to CCM in synthetic data simulation as well as in empirical electroencephelography (EEG) and functional near infrared spectroscopy (fNIRS) activity data. Our findings show that GP-CCM provides a statistic that consistently reports indirect causal structures in non-separable unidirectional system interactions; GP-CCM also provides coupling direction estimates in noisy physiological signals, showing that EEG likely causes, i.e., drives, fNIRS dynamics.