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arXiv · 2403.16575

A Measure of Synergy based on Union Information

André F. C. Gomes·Mário A. T. Figueiredo
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Abstract

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information - which quantifies the information that is present in at least one of the sources - from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature.

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André F. C. Gomes, Mário A. T. Figueiredo. 2024-03-25. A Measure of Synergy based on Union Information. https://doi.org/10.3390/e26030271

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