Quantifying high-order interdependencies via multivariate extensions of the mutual information

Area of Science:

• Complex systems analysis
• Information theory
• Statistical mechanics

Background:

• Emergence describes phenomena where large-scale patterns are not predictable from lower-level components.
• Quantifying high-order interactions and emergence is challenging in complex systems.
• Existing metrics often require defining 'predictors' and 'targets,' limiting their scope.

Purpose of the Study:

• Introduce a model-agnostic framework to study statistical synergy.
• Develop and analyze the O-information as a novel metric for characterizing synergy and redundancy.
• Explore the applicability of statistical synergy in diverse fields.

Main Methods:

• Leveraging multivariate extensions of Shannon's mutual information.
• Introducing and defining the O-information as a symmetric measure of high-order interactions.
• Analyzing the mathematical properties of O-information and its relation to existing metrics.

Main Results:

• The O-information quantifies statistical synergy, distinguishing between synergy- and redundancy-dominated systems.
• O-information is a symmetric metric, assessing intrinsic system properties without predefined roles.
• Demonstrated the framework's utility through an analysis of Baroque music scores.

Conclusions:

• The O-information provides a powerful, model-agnostic tool for studying emergence and complex interactions.
• This metric advances the understanding of systems where large-scale properties arise from intricate, high-order relationships.
• The approach has broad applicability, from statistical mechanics and neuroscience to the arts.