Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information

2019/02/28 by Fernando Rosas, Pedro A. M. Mediano, Michael Gastpar +1 · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #cs.IT #math.IT #q-bio.NC

paper · pdf · doi:10.1103/physreve.100.032305

published as Phys. Rev. E 100, 032305 (2019)

arxiv created 2019/02/28 · arxiv updated 2019/09/18

Abstract

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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