Redundant variables and Granger causality

TL;DR

This paper examines how redundant variables affect multivariate Granger causality analysis, proposing methods to group redundancies and applying these to neurological data to reveal changes in brain information patterns.

Contribution

It introduces two novel approaches for grouping redundant variables in causality analysis and demonstrates their application to neurological data.

Findings

Redundant variables cause under-estimation of causality in standard analysis.

Proposed grouping methods improve causality detection in the presence of redundancy.

Application reveals changes in brain information patterns after stimulation.

Abstract

We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.