Measuring Information Transfer Between Nodes in a Brain Network through Spectral Transfer Entropy

Brain connectivity reflects how different regions of the brain interact during performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), this may be explored via an information-theoretic causal measure, called transfer entropy (TE), which does not impose any distributional assumption on the variables and covers any form of relationship (beyond linear) between them. To improve utility of TE in brain signal analysis, we propose a novel methodology to capture cross-channel information transfer in the frequency domain. Specifically, we introduce a new causal measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a certain frequency-band oscillation of a channel to an oscillation of another channel. In contrast with previous works on TE in the frequency domain, we differentiate our work by considering an extreme value perspective that employs the maximum magnitude of filtered series within time blocks. The main advantages of our proposed approach is that it is robust to the inherent problems of linear filtering and allows adjustments for multiple comparisons to control family-wise error rate (FWER). Another novel contribution is a simple yet efficient estimation method based on the combination vine copulas and extreme value theory that enables estimates to capture zero (boundary point) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, making significance testing for STE straightforward through a standard resampling approach. Lastly, we illustrate the advantage of our proposed measure through some numerical experiments and provide interesting and novel findings on the analysis of EEG recordings linked to a visual task.