Higher-order Common Information
<|reference_start|>Higher-order Common Information: 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.<|reference_end|>
@article{østergaard2024higher-order,
    title={Higher-order Common Information},
    author={Jan {O}stergaard},
    journal={arXiv preprint arXiv:2406.02001},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.02001},
    primaryClass={cs.IT math.IT}
}