  Pairwise metrics are often employed to estimate statistical dependencies
between brain regions, however they do not capture higher-order information
interactions. It is critical to explore higher-order interactions that go
beyond paired brain areas in order to better understand information processing
in the human brain. To address this problem, we applied multivariate mutual
information, specifically, Total Correlation and Dual Total Correlation to
reveal higher-order information in the brain. In this paper, we estimate these
metrics using matrix-based R\'enyi's entropy, which offers a direct and easily
interpretable approach that is not limited by direct assumptions about
probability distribution functions of multivariate time series. We applied
these metrics to resting-state fMRI data in order to examine higher-order
interactions in the brain. Our results showed that the higher-order information
interactions captured increase gradually as the interaction order increases.
Furthermore, we observed a gradual increase in the correlation between the
Total Correlation and Dual Total Correlation as the interaction order
increased. In addition, the significance of Dual Total Correlation values
compared to Total Correlation values also indicate that the human brain
exhibits synergy dominance during the resting state.
