High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. This paper presents a framework to measure high-order interdependence that disentangles their effect on each individual pattern exhibited by a multivariate system. The approach is centred on the 'local O-information', a new measure that assesses the balance between synergistic and redundant interdependencies at each pattern. To illustrate the potential of this framework, we present a detailed analysis of music scores from J.S. Bach, which reveals how high-order interdependence is deeply connected with highly non-trivial aspects of the musical discourse. Our results place the local O-information as a promising tool of wide applicability, which opens new perspectives for analysing high-order relationships in the patterns exhibited by complex systems.
@article{arxiv.2108.11625,
title = {Quantifying high-order interdependencies on individual patterns via the local O-information: theory and applications to music analysis},
author = {Tomas Scagliarini and Daniele Marinazzo and Yike Guo and Sebastiano Stramaglia and Fernando E. Rosas},
journal= {arXiv preprint arXiv:2108.11625},
year = {2022}
}