Evaluation of mutual information estimators on nonlinear dynamic systems

TL;DR

This study evaluates the accuracy and stability of various mutual information estimators, including histogram-based, k-nearest neighbors, and kernel methods, on nonlinear dynamical systems through Monte Carlo simulations.

Contribution

It provides a comprehensive comparison of mutual information estimators, highlighting the superior stability of the k-nearest neighbor approach in nonlinear time series analysis.

Findings

k-nearest neighbor estimator is most stable

Estimators converge to a stable value with increasing data

Degree of deviation varies among estimators

Abstract

Mutual information is a nonlinear measure used in time series analysis in order to measure the linear and non-linear correlations at any lag $\tau$. The aim of this study is to evaluate some of the most commonly used mutual information estimators, i.e. estimators based on histograms (with fixed or adaptive bin size), $k$-nearest neighbors and kernels. We assess the accuracy of the estimators by Monte-Carlo simulations on time series from nonlinear dynamical systems of varying complexity. As the true mutual information is generally unknown, we investigate the existence and rate of consistency of the estimators (convergence to a stable value with the increase of time series length), and the degree of deviation among the estimators. The results show that the $k$-nearest neighbor estimator is the most stable and less affected by the method-specific parameter.