Reducing the Bias of Causality Measures

TL;DR

This paper introduces bias reduction techniques for causality measures in time series, improving their accuracy in detecting true causal effects and correctly identifying the absence of causality, validated on simulations and EEG data.

Contribution

It proposes a bias correction method using surrogate data for causality measures, enhancing their reliability across various settings and applications.

Findings

Corrected measures stabilize at zero when no causality exists.

Correctly detect the direction of information flow in simulated systems.

Effectively applied to EEG data for brain connectivity analysis.

Abstract

Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted, in view of the results from the simulation study.