🤖 AI Summary
This work addresses the long-standing problem in partial information decomposition (PID) that synergistic information lacks a rigorous, computable definition. We propose a novel union information measure grounded in communication channel modeling—the first such channel-theoretic approach integrated into the PID framework. The measure satisfies the foundational axioms of minimality, monotonicity, and continuity, thereby yielding a unique, analytically tractable synergistic information quantity. Evaluated on canonical PID benchmark examples, our measure more accurately captures multivariate synergy than established alternatives such as (I_{min}) and (I_{ ext{proj}}), balancing theoretical soundness with computational feasibility. Beyond introducing the new measure, this work critically reexamines and systematically reconstructs the conceptual foundations of union and synergistic information representation in PID. The resulting framework provides an interpretable, reproducible analytical tool for synergy quantification, with direct applicability to neuroscience, complex systems analysis, and other domains requiring principled multivariate dependency assessment.
📝 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.