Robustly estimating the flow direction of information in complex physical systems

TL;DR

This paper introduces a new phase spectrum-based measure for estimating information flow direction in complex systems, which is robust to noise, mixtures, and non-linear phase spectra, outperforming traditional methods in simulations and EEG data analysis.

Contribution

The paper presents a novel Phase Slope Index that accurately estimates information flow direction, with invariance properties suitable for real-world physical and biological systems.

Findings

The measure detects true unidirectional information flow as effectively as Granger causality.

It correctly identifies non-significant results in mixed independent sources, unlike Granger causality.

EEG analysis shows a consistent front-to-back information flow across subjects.

Abstract

We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a) it is strictly insensitive to mixtures of arbitrary independent sources, (b) it gives meaningful results even if the phase spectrum is not linear, and (c) it properly weights contributions from different frequencies. Simulations of a class of coupled multivariate random data show that for truly unidirectional information flow without additional noise contamination our measure detects the correct direction as good as the standard Granger causality. For random mixtures of independent sources Granger Causality erroneously yields highly significant results whereas our measure correctly becomes non-significant. An application of our novel method to EEG data (88 subjects in eyes-closed condition) reveals a strikingly clear front-to-back information flow in the vast majority of subjects and thus contributes to a better understanding of information processing in the brain.