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arXiv · 2108.11625

Quantifying high-order interdependencies on individual patterns via the local O-information: theory and applications to music analysis

Tomas Scagliarini·Daniele Marinazzo·Yike Guo·Sebastiano Stramaglia·Fernando E. Rosas
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Abstract

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.

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Tomas Scagliarini, Daniele Marinazzo, Yike Guo, Sebastiano Stramaglia, Fernando E. Rosas. 2021-08-26. Quantifying high-order interdependencies on individual patterns via the local O-information: theory and applications to music analysis. https://doi.org/10.1103/physrevresearch.4.013184

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