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

TL;DR

This paper introduces the local O-information, a novel measure for quantifying high-order interdependencies in complex systems, demonstrated through analysis of Bach's music scores to reveal intricate interdependence patterns.

Contribution

The paper develops the local O-information framework to analyze high-order interdependencies at the pattern level, with applications to music analysis.

Findings

High-order interdependence is linked to complex musical discourse.

The local O-information effectively captures synergistic and redundant relationships.

Application to Bach's scores demonstrates the measure's utility in real-world data.

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.