Higher-order Common Information

We present a new notion R_ of higher-order common information, which quantifies the information that ≥ 2 arbitrarily distributed random variables have in common. We provide analytical lower bounds on R₃ and R₄ for jointly Gaussian distributed sources and provide computable lower bounds for R_ for any and any sources. We also provide a practical method to estimate the lower bounds on, e.g., real-world time-series data. As an example, we consider EEG data acquired in a setup with competing acoustic stimuli. We demonstrate that R₃ has descriptive properties that is not in R₂. Moreover, we observe a linear relationship between the amount of common information R₃ communicated from the acoustic stimuli and to the brain and the corresponding cortical activity in terms of neural tracking of the envelopes of the stimuli.