Gradients of O-information: low-order descriptors of high-order dependencies

TL;DR

This paper introduces gradients of the O-information metric as low-order descriptors to localize high-order dependencies among variables, demonstrated through Ising models and macroeconomic data.

Contribution

It proposes a novel gradient-based approach to analyze high-order information sharing, complementing the global O-information metric.

Findings

Gradients effectively identify key variables in high-order informational structures.

Application to Ising models reveals specific spins' roles in system dependencies.

Analysis of macroeconomic data demonstrates practical utility in real-world systems.

Abstract

O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here we propose the gradients of the O-information as low-order descriptors that can characterise how high-order effects are localised across a system of interest. We illustrate the capabilities of the proposed framework by revealing the role of specific spins in Ising models with frustration, and on practical data analysis on US macroeconomic data. Our theoretical and empirical analyses demonstrate the potential of these gradients to highlight the contribution of variables in forming high-order informational circuits