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Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information
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This article introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric capable of characterising synergy- and redundancy-dominated systems. We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we use the proposed framework to explore the relevance of statistical synergy in Baroque music scores.
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The many faces of multivariate information
Three well-known multivariate information measures are unified as members of a one-parameter family Δ^k, whose sign is claimed to track the order of dominant interactions.
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