We present a new notion $R_\ell$ of higher-order common information, which quantifies the information that $\ell\geq 2$ arbitrarily distributed random variables have in common. We provide analytical lower bounds on $R_3$ and $R_4$ for jointly Gaussian distributed sources and provide computable lower bounds for $R_\ell$ for any $\ell$ 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 $R_3$ has descriptive properties that is not in $R_2$. Moreover, we observe a linear relationship between the amount of common information $R_3$ 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.

翻译：我们提出了一种新的高阶公共信息概念 $R_\ell$，用于量化 $\ell\geq 2$ 个任意分布的随机变量所共有的信息。我们针对联合高斯分布信源给出了 $R_3$ 和 $R_4$ 的解析下界，并为任意 $\ell$ 和任意信源提供了可计算的下界。我们还提出了一种实用方法来估计下界，例如在现实世界的时间序列数据上。作为一个示例，我们考虑了在竞争性听觉刺激设置下采集的脑电图数据。我们证明 $R_3$ 具有 $R_2$ 所不具备的描述特性。此外，我们观察到从听觉刺激传递到大脑的公共信息量 $R_3$ 与相应的皮层活动（表现为对刺激包络的神经追踪）之间存在线性关系。