Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Abstract

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone.

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Cited by in corpus (13)

• Networks beyond pairwise interactions: structure and dynamics
• Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information
• Pointwise Partial Information Decomposition using the Specificity and Ambiguity Lattices
• Multiscale Information Storage of Linear Long-Range Correlated Stochastic Processes
• Generalised Measures of Multivariate Information Content
• Detecting causality in multivariate time series via non-uniform embedding
• Estimating Conditional Transfer Entropy in Time Series using Mutual Information and Non-linear Prediction
• Local Granger Causality
• Exact partial information decompositions for Gaussian systems based on dependency constraints
• The identity of information: how deterministic dependencies constrain information synergy and redundancy
• Interplay of synergy and redundancy in diamond motif
• MAXENT3D_PID: An Estimator for the Maximum-entropy Trivariate Partial Information Decomposition
• Multiscale Partial Information Decomposition of Dynamic Processes with Short and Long-range correlations: Theory and Application to Cardiovascular Control