Non-parametric test for connectivity detection in multivariate autoregressive networks and application to multiunit activity data

Directed connectivity inference has become a cornerstone in neuroscience following the recent progress in neuroimaging and elctrophysiological techniques to characterize anatomical and functional networks. This paper focuses on the detection of existing connections from the observed activity in networks of 50 to 150 nodes with linear feedback in discrete time. Through the variation of multiple network parameters, our numerical results indicate that directed connections - in the time domain - are more accurately estimated based on the coefficients obtained from multivariate autoregressive (MVAR) than Granger causality analysis, which is based on the error residuals of the same MVAR linear regression. Based on these findings, we propose a non-parametric significance test for connectivity detection, which achieves a good control of false positives (type 1 error) and is robust to various network topologies. When generating surrogate distributions, we compare the effects of circular shifts, random permutations and phase randomization of the observed time series, each breaking down covariances in a specific manner: the MVAR estimates from those shuffled covariances build a null-hypothesis distribution for each connection, from which the original connectivity estimate can be compared. We apply our method to multiunit activity data recorded from Utah electrode arrays in monkey and examine the detected interactions between 25 channels for a proof of concept. The results unravel a non-trivial underlying connectivity structure, which differentiates the effect of incoming and outgoing connections.