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 prevalently 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.
Highlights
The information-theoretic treatment of groups of correlated degrees of freedom can reveal their functional roles as memory structures or information processing units
These elements essentially reflect the new information produced at each moment in time about a target system in the network [2], the information stored in the target system [3,4], the information transferred to it from the other connected systems [5,6] and the modification of the information flowing from multiple source systems to the target [7,8]
The theoretical derivations are first used in examples of benchmark Gaussian systems, reporting that these systems may generate patterns of information decomposition characterized by prevalently redundant or synergistic information transfer persisting across multiple time scales or even by alternating the prevalence of redundant and synergistic source interaction depending on the time scale
Summary
The information-theoretic treatment of groups of correlated degrees of freedom can reveal their functional roles as memory structures or information processing units. Both the problems of defining appropriate PID measures and of reliably estimating these measures from data are much alleviated if one assumes that the observed variables have a joint Gaussian distribution In such a case, recent studies have proven the equivalence between most of the proposed redundancy measures to be used in the PID [36] and have provided closed form solutions to the issue of computing any measure of information dynamics from the parameters of the vector autoregressive (VAR) model that characterizes an observed multivariate. We aim at extending these recent theoretical advances to the multiscale analysis of information modification in multivariate Gaussian systems performed through the IID and PID decomposition frameworks To this end, we exploit the theory of state space (SS) models [50] and build on recent theoretical results [44,45] to show that exact values of interaction transfer, as well as redundant and synergistic transfer can be obtained for coupled. The proposed framework is implemented in the msID MATLAB R toolbox, which is uploaded as
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