Using time-delayed mutual information to discover and interpret temporal correlation structure in complex populations

TL;DR

This paper introduces a method using time-delayed mutual information to analyze and interpret the correlation structure in complex, heterogeneous populations of time-series data, with applications to medical data.

Contribution

It develops practical information-theoretic calculations to compare population-level and aggregated mutual information, revealing population heterogeneity and composition.

Findings

Applied to glucose time series, revealing population heterogeneity.

Demonstrated method's applicability to diverse, non-stationary data.

Provided insights into physiological features of subpopulations.

Abstract

This paper addresses how to calculate and interpret the time-delayed mutual information for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle used for this analysis is a comparison between the time-delayed mutual information averaged over the population and the time-delayed mutual information of an aggregated population (here aggregation implies the population is conjoined before any statistical estimates are implemented). Through the use of information theoretic tools, a sequence of practically implementable calculations are detailed that allow for the average and aggregate time-delayed mutual information to be interpreted. Moreover, these calculations can be also be used to understand the degree of homo- or heterogeneity present in the population. To demonstrate that the proposed methods can be used in nearly any situation, the methods are applied and demonstrated on the time series of glucose measurements from two different subpopulations of individuals from the Columbia University Medical Center electronic health record repository, revealing a picture of the composition of the population as well as physiological features.