Reducing the bias of causality measures

Abstract

Measures of the direction and strength of the interdependence between two time series are evaluated and modified 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 a 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.

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

“…This constitutes a main direction for further research, because real-world processes display very often non-Gaussian distributions, which would make an extension to nonlinear models or model-free approaches beneficial. The questions that are still open in this respect include the evaluation of proper theoretical definitions of synergy or redundancy for nonlinear processes [25][26][27][28][29], the development of reliable entropy estimators for multivariate variables with different dimensions [6,35,61] and the assessment of the extent to which non-linear model-free methods really outperform the linear model-based approach adopted here and in previous investigations [62].…”

Simulation Study of Direct Causality Measures in Multivariate Time Series

“…Most comparative works on the effectiveness of causality measures concentrate on bivariate tests, e.g., [33][34][35][36], while some works evaluating multivariate methodologies include only model-based tests, see, e.g., [37][38][39], or compare direct and indirect causality measures, e.g., [36,40].…”

Structure of a Global Network of Financial Companies Based on Transfer Entropy

“…A measure that has been used in a variety of fields, and which is both dynamic and non-symmetric, is Transfer Entropy, developed by Schreiber [39] and based on the concept of Shannon Entropy, first developed in the theory of information by Shannon [40]. Transfer entropy has been used in the study of cellular automata in Computer Science [41][42][43], in the study of the neural cortex of the brain [44][45][46][47][48][49], in the study of social networks [50], in Statistics [51][52][53][54], and in dynamical systems [55][56][57], and received a thermodynamic interpretation in [58].…”