Assessing Coupling Dynamics from an Ensemble of Time Series

Abstract

Finding interdependency relations between time series provides valuable knowledge about the processes that generated the signals. Information theory sets a natural framework for important 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 partly alleviated 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 generated by coupled electronic circuits that Entropy 2015, 17 1959 the proposed approach allows one to recover the time-resolved dynamics of the coupling between different subsystems.

Contribution to Transfer Entropy Estimation via the k-Nearest-Neighbors Approach

“…,k is projected into the other three lower dimensional spaces, leading to the standard TE estimator [25,27,28] (implementation available in the TRENTOOL toolbox, Version 3.0, Box 10 in Figure 1):…”

“…Note that a generalization of Equation (21) was proposed in [28] to extend this formula to the estimation of entropy combinations other than MI and TE.…”

“…The strategy was to constrain the three corresponding (hyper-)cubes, including nearest neighbors, respectively in spaces S X , S Y and S X,Y , to have an identical edge length (the idea of projected distances, Box 14 ) for a better cancellation of the three corresponding biases. The same approach was used to derive the standard TE estimator [25][26][27][28][29] (Box 10 ), which has been implemented in the TRENTOOL toolbox, Version 3.0. In [24], Kraskov et al also suggested, for MI estimation, to replace minimal (hyper-)cubes with smaller minimal (hyper-)rectangles equal to the product of two minimal (hyper-)cubes built separately in subspaces S X and S Y (KSG MI Estimator 2, Box 12 ) to exploit more efficiently the Kozachenko-Leonenko approach.…”

A Recipe for the Estimation of Information Flow in a Dynamical System

“…It has been demonstrated [36] that no fine tuning of specific parameters is necessary unlike the case of the adaptive partitioning method of Darbellay and Vajda [35] and the efficiency of the method has been shown for Gaussian and three other non-Gaussian distributed data sets. Herrero et al extended this technique to TE in [37] and this has been utilized in many applications where TE is estimated [38][39][40] due to its advantages.…”

Identicação de sistemas neurais com redes bayesianas dinâmicas e transferência de entropia

“…A princípio, a forma mais comum de se lidar com sinais não-estacionários é repetir um experimento várias vezes e realizar-se medidas nos dados em mesmos instantes de tempo (mé-todos de ensemble, por exemplo, são eficientes neste objetivo (Gómez-Herrero et al, 2015)). …”