Expanding the Transfer Entropy to Identify Information Subgraphs in Complex Systems

TL;DR

This paper extends transfer entropy to identify key variable groups in complex systems, revealing informational circuits with applications demonstrated on EEG data sets.

Contribution

It introduces a formal expansion of transfer entropy to detect irreducible variable sets and informational circuits, assuming Gaussianity for computational efficiency.

Findings

Identified informational circuits in EEG data

Validated the method on two EEG datasets

Provided a computationally feasible approach for complex systems

Abstract

We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to informational circuits present in the system, with an informational character which can be associated to the sign of the contribution. For the sake of computational complexity, we adopt the assumption of Gaussianity and use the corresponding exact formula for the conditional mutual information. We report the application of the proposed methodology on two EEG data sets.