Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems

Abstract

To fully characterize the information that two `source' variables carry about a third `target' variable, one must decompose the total information into redundant, unique and synergistic components, i.e. obtain a partial information decomposition (PID). However Shannon's theory of information does not provide formulae to fully determine these quantities. Several recent studies have begun addressing this. Some possible definitions for PID quantities have been proposed, and some analyses have been carried out on systems composed of discrete variables. Here we present the first in-depth analysis of PIDs on Gaussian systems, both static and dynamical. We show that, for a broad class of Gaussian systems, previously proposed PID formulae imply that: (i) redundancy reduces to the minimum information provided by either source variable, and hence is independent of correlation between sources; (ii) synergy is the extra information contributed by the weaker source when the stronger source is known, and can either increase or decrease with correlation between sources. We find that Gaussian systems frequently exhibit net synergy, i.e. the information carried jointly by both sources is greater than the sum of informations carried by each source individually. Drawing from several explicit examples, we discuss the implications of these findings for measures of information transfer and information-based measures of complexity, both generally and within a neuroscience setting. Importantly, by providing independent formulae for synergy and redundancy applicable to continuous time-series data, we open up a new approach to characterizing and quantifying information sharing amongst complex system variables.

29 pages, 4 figures, in press Physical Review E, minor revisions to original version in response to peer review

References in corpus (6)

• Nonnegative Decomposition of Multivariate Information
• Multivariate Granger Causality and Generalized Variance
• The functional structure of cortical neuronal networks grown in vitro
• Synergy and redundancy in the Granger causal analysis of dynamical networks
• On the Dynamical Complexity of Small-World Networks of Spiking Neurons
• Identification of functional information subgraphs in complex networks

Cited by in corpus (25)

• Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes
• Integrated information as a common signature of dynamical and information-processing complexity
• Invariant components of synergy, redundancy, and unique information among three variables
• Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems
• Towards an extended taxonomy of information dynamics via Integrated Information Decomposition
• Secret Sharing and Shared Information
• Quantifying how much sensory information in a neural code is relevant for behavior
• Decomposing past and future: Integrated information decomposition based on shared probability mass exclusions
• Quantifying high-order interdependencies on individual patterns via the local O-information: theory and applications to music analysis
• Synergy as a warning sign of transitions: the case of the two-dimensional Ising model
• The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal
• An information-theoretic approach to hypergraph psychometrics
• Assessing high-order effects in feature importance via predictability decomposition
• A partial information decomposition for discrete and continuous variables
• Partial Information Decomposition via Deficiency for Multivariate Gaussians
• The coherent feed-forward loop acts as an efficient information transmitting motif
• Integrated Information Decomposition Unveils Major Structural Traits of $In$ $Silico$ and $In$ $Vitro$ Neuronal Networks
• Orders between channels and implications for partial information decomposition
• A Measure of Synergy based on Union Information
• Information Synergy in the Anticipatory Dynamics of a Retina
• Multivariate Partial Information Decomposition: Constructions, Inconsistencies, and Alternative Measures
• Disentanglement Analysis with Partial Information Decomposition
• An Approximation Scheme for Multivariate Information based on Partial Information Decomposition
• Information transmission in a two-step cascade: Interplay of activation and repression
• Multiscale Partial Information Decomposition of Dynamic Processes with Short and Long-range correlations: Theory and Application to Cardiovascular Control