Kernel method for nonlinear Granger causality

TL;DR

This paper introduces a kernel-based method to detect nonlinear Granger causality in complex systems, enabling analysis of nonlinearity in time series data with improved overfitting control.

Contribution

It generalizes linear Granger causality to the nonlinear domain using reproducing kernel Hilbert spaces, with a novel overfitting mitigation strategy.

Findings

Effective detection of nonlinear causal relationships in chaotic maps.

Application to physiological data demonstrates practical utility.

Method outperforms linear approaches in complex systems.

Abstract

Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to reach a deeper comprehension of phenomena ranging from turbulent fluids to neural networks, as well as complex physiological signals. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.