Assessing coupling dynamics from an ensemble of time series

TL;DR

This paper introduces a data-efficient, ensemble-based estimator for time-resolved information-theoretic measures that accurately captures dynamic interdependencies in multivariate time series.

Contribution

It presents a novel ensemble approach that improves estimation of time-varying dependencies, overcoming limitations of traditional methods with brief or evolving signals.

Findings

Enhanced accuracy in estimating mutual information and transfer entropy.

Successful application to simulated data demonstrating dynamic coupling recovery.

Effective analysis of real data revealing time-resolved interdependencies.

Abstract

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several classes of statistical dependencies. However, a reliable estimation from information-theoretic functionals is hampered when the dependency to be assessed is brief or evolves in time. Here, we show that these limitations can be overcome when we have access to an ensemble of independent repetitions of the time series. In particular, we gear a data-efficient estimator of probability densities to make use of the full structure of trial-based measures. By doing so, we can obtain time-resolved estimates for a family of entropy combinations (including mutual information, transfer entropy, and their conditional counterparts) which are more accurate than the simple average of individual estimates over trials. We show with simulated and real data that the proposed approach allows to recover the time-resolved dynamics of the coupling between different subsystems.