Estimation of time-delayed mutual information and bias for irregularly and sparsely sampled time-series

TL;DR

This paper introduces a new method to estimate the bias in time-delayed mutual information for irregularly sampled time-series, improving correlation analysis in complex systems.

Contribution

It proposes a novel bias estimation technique for time-delayed mutual information applicable to irregular and sparse data, validated on Lorenz and medical time series.

Findings

Bias estimation aligns with mutual information between distant data distributions.

Method performs well on Lorenz system data.

Effective on real-world glucose time series.

Abstract

A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be equivalent to the mutual information between two distributions of points from the same system separated by infinite time. Thus intuitively, estimation of the bias is reduced to estimation of the mutual information between distributions of data points separated by large time intervals. The proposed bias estimation techniques are shown to work for Lorenz equations data and glucose time series data of three patients from the Columbia University Medical Center database.