The primary method for evaluating high-order brain interactions using information-theoretic measures such as (dual) total correlation and O-information involves the Gaussian approximation. Although this approximation is rather accurate for functional MRI signals, it is unclear whether this holds for electroencephalography (EEG) and magnetoencephalography (MEG) signals. Here, we introduce the elliptical approximation, which is valid for Gaussian data and a large family of non-Gaussian data. To illustrate its use, we applied both approximations to EEG and MEG signals and found that the Gaussian approximation to the (dual) total correlation and O-information is quite accurate for physiological resting-state oscillations, but is highly inaccurate for EEG data recorded during an absence seizure. 
In particular, for interactions of high-order (> 10) the approximations do not always agree on whether the interactions are dominated by synergy or redundancy. Thus, our proposed method offers an opportunity to study high-order interactions in electrophysiological brain activity.