# Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

## TL;DR

This paper introduces an exact analytical method to compute multiscale information transfer, redundancy, and synergy in coupled Gaussian processes, with applications in neuroscience and benchmark systems.

## Contribution

It derives closed-form expressions for information decomposition terms at multiple time scales using state space models, enabling detailed analysis of multiscale interactions.

## Key findings

- Gaussian systems show persistent redundant or synergistic information transfer across scales.
- The method reveals alternating dominance of redundancy and synergy depending on the time scale.
- Applied to epilepsy networks, it detects multiscale causal interactions related to seizures.

## 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.