Assessing the relative importance of high-order interactions versus dyadic relations

Determine a quantitative framework to assess the relative importance of high-order (polyadic) interactions among components of complex systems compared to dyadic (pairwise) relations, so as to evaluate how multi-variable dependencies contribute to observed information flow relative to two-variable dependencies.

Background

The paper discusses limitations of dyadic analyses such as pairwise Transfer Entropy (TE) and Granger causality (GC) in the presence of high-order dependencies like redundancy and synergy. Within this context, the authors note that existing approaches often neglect polyadic relationships, motivating the need to explicitly compare their contributions against dyadic relations.

To address this need, the paper proposes a decomposition of TE by searching for conditioning sets that minimize or maximize TE, thereby partitioning information flow into unique, redundant, and synergistic components. This is presented as a way to quantify many-body effects, highlighting the underlying open question of how to systematically and quantitatively assess the relative importance of high-order interactions compared to dyadic ones.