Dimension reduction of frequency-based direct Granger causality measures on short time series

Abstract

Background: The mainstream in the estimation of effective brain connectivity relies on Granger causality measures in the frequency domain. If the measure is meant to capture direct causal effects accounting for the presence of other observed variables, as in multi-channel electroencephalograms (EEG), typically the fit of a vector autoregressive (VAR) model on the multivariate time series is required. For short time series of many variables, the estimation of VAR may not be stable requiring dimension reduction resulting in restricted or sparse VAR models.

New method: The restricted VAR obtained by the modified backward-in-time selection method (mBTS) is adapted to the generalized partial directed coherence (GPDC), termed restricted GPDC (RGPDC). Dimension reduction on other frequency based measures, such the direct directed transfer function (dDTF), is straightforward.

Results: First, a simulation study using linear stochastic multivariate systems is conducted and RGPDC is favorably compared to GPDC on short time series in terms of sensitivity and specificity. Then the two measures are tested for their ability to detect changes in brain connectivity during an epileptiform discharge (ED) from multi-channel scalp EEG.

Comparison with existing method(s): It is shown that RGPDC identifies better than GPDC the connectivity structure of the simulated systems, as well as changes in the brain connectivity, and is less dependent on the free parameter of VAR order.

Conclusions: The proposed dimension reduction in frequency measures based on VAR constitutes an appropriate strategy to estimate reliably brain networks within short-time windows.

Keywords: Direct Granger causality; Electroencephalograms; Epileptiform discharges; Generalized partial directed coherence (GPDC); Restricted or sparse VAR models.