Estimation Of Transfer Entropy Research Articles

Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series

BackgroundThe detection of change in magnitude of directional coupling between two non-linear time series is a common subject of interest in the biomedical domain, including studies involving the respiratory chemoreflex system. Although transfer entropy is a useful tool in this avenue, no study to date has investigated how different transfer entropy estimation methods perform in typical biomedical applications featuring small sample size and presence of outliers.MethodsWith respect to detection of increased coupling strength, we compared three transfer entropy estimation techniques using both simulated time series and respiratory recordings from lambs. The following estimation methods were analyzed: fixed-binning with ranking, kernel density estimation (KDE), and the Darbellay-Vajda (D-V) adaptive partitioning algorithm extended to three dimensions. In the simulated experiment, sample size was varied from 50 to 200, while coupling strength was increased. In order to introduce outliers, the heavy-tailed Laplace distribution was utilized. In the lamb experiment, the objective was to detect increased respiratory-related chemosensitivity to O2 and CO2 induced by a drug, domperidone. Specifically, the separate influence of end-tidal PO2 and PCO2 on minute ventilation before and after administration of domperidone was analyzed.ResultsIn the simulation, KDE detected increased coupling strength at the lowest SNR among the three methods. In the lamb experiment, D-V partitioning resulted in the statistically strongest increase in transfer entropy post-domperidone for . In addition, D-V partitioning was the only method that could detect an increase in transfer entropy for , in agreement with experimental findings.ConclusionsTransfer entropy is capable of detecting directional coupling changes in non-linear biomedical time series analysis featuring a small number of observations and presence of outliers. The results of this study suggest that fixed-binning, even with ranking, is too primitive, and although there is no clear winner between KDE and D-V partitioning, the reader should note that KDE requires more computational time and extensive parameter selection than D-V partitioning. We hope this study provides a guideline for selection of an appropriate transfer entropy estimation method.

Distinguishing Anticipation from Causality: Anticipatory Bias in the Estimation of Information Flow

We report that transfer entropy estimates obtained from low-resolution and/or small data sets show net information flow away from a purely anticipatory element whereas transfer entropy calculated using exact distributions show the flow towards it. This means that for real-world data sets anticipatory elements can appear to be strongly driving the network dynamics even when there is no possibility of such an influence. Furthermore, we show that in the low-resolution limit there is no statistic that can distinguish anticipatory elements from causal ones.

Testing methodologies for the nonlinear analysis of causal relationships in neurovascular coupling

We investigated the use and implementation of a nonlinear methodology for establishing which changes in neurophysiological signals cause changes in the blood oxygenation level-dependent (BOLD) contrast measured in functional magnetic resonance imaging. Unlike previous analytical approaches, which used linear correlation to establish covariations between neural activity and BOLD, we propose a directed information-theoretic measure, the transfer entropy, which can elucidate even highly nonlinear causal relationships between neural activity and BOLD signal. In this study we investigated the practicality of such an analysis given the limited data samples that can be collected experimentally due to the low temporal resolution of BOLD signals. We implemented several algorithms for the estimation of transfer entropy and we tested their effectiveness using simulated local field potentials (LFPs) and BOLD data constructed to match the main statistical properties of real LFP and BOLD signals measured simultaneously in monkey primary visual cortex. We found that using the advanced methods of entropy estimation implemented and described here, a transfer entropy analysis of neurovascular coupling based on experimentally attainable data sets is feasible.

Exploring transient transfer entropy based on a group-wise ICA decomposition of EEG data

This paper presents a data-driven pipeline for studying asymmetries in mutual interdependencies between distinct components of EEG signal. Due to volume conductance, estimating coherence between scalp electrodes may lead to spurious results. A group-based independent component analysis (ICA), which is conducted across all subjects and conditions simultaneously, is an alternative representation of the EEG measurements. Within this approach, the extracted components are independent in a global sense while short-lived or transient interdependencies may still be present between the components. In this paper, functional roles of the ICA components are specified through a partial least squares (PLS) analysis of task effects within the time course of the derived components. Functional integration is estimated within the information-theoretic approach using transfer entropy analysis based on asymmetries in mutual interdependencies of reconstructed phase dynamics. A secondary PLS analysis is performed to assess robust task-specific changes in transfer entropy estimates between functionally specific components.

Information Flow and Application to Epileptogenic Focus Localization From Intracranial EEG

Transfer entropy ( TE) is a recently proposed measure of the information flow between coupled linear or nonlinear systems. In this study, we suggest improvements in the selection of parameters for the estimation of TE that significantly enhance its accuracy and robustness in identifying the direction and the level of information flow between observed data series generated by coupled complex systems. We show the application of the improved TE method to long (in the order of days; approximately a total of 600 h across all patients), continuous, intracranial electroencephalograms (EEG) recorded in two different medical centers from four patients with focal temporal lobe epilepsy (TLE) for localization of their foci. All patients underwent ablative surgery of their clinically assessed foci. Based on a surrogate statistical analysis of the TE results, it is shown that the identified potential focal sites through the suggested analysis were in agreement with the clinically assessed sites of the epileptogenic focus in all patients analyzed. It is noteworthy that the analysis was conducted on the available whole-duration multielectrode EEG, that is, without any subjective prior selection of EEG segments or electrodes for analysis. The above, in conjunction with the use of surrogate data, make the results of this analysis robust. These findings suggest a critical role TE may play in epilepsy research in general, and as a tool for robust localization of the epileptogenic focus/foci in patients with focal epilepsy in particular.

Effects of noise on transfer entropy estimation for damage detection

Recent research has shown that transfer entropy can be effectively employed as a feature for nonlinearity detection and linear damage identification. However, computation of transfer entropy requires the estimation of non-parametric one-, two-, and three-dimensional probability density functions. Therefore, small random perturbations caused by noise could lead to large variances in transfer entropy estimates. In this paper, we evaluate the effect of input and output noise on estimation of transfer entropy, and how noise, in turn, affects the capability of transfer entropy as a damage detector in a structural health monitoring (SHM) application. A damage index from the transfer entropy is computed from the response of a simulated multi-degree-of-freedom oscillator subject to linear and nonlinear stiffness changes in the presence of various noise influences. Damage indices are also evaluated for an experimental frame structure. Based on the computational study, we find that input noise lessens the sensitivity of the damage feature by diminishing the ability of the non-parametric density estimators to produce low variance transfer entropy estimations. Despite this reduced capability, an input that has no deterministic component can still detect a 25% stiffness loss in the computational example employed. Output noise has a greater impact on the feature's ability to accurately estimate the transfer entropy, such that a signal-to-noise threshold of approximately 30 dB leads to a greatly diminished ability to detect damage. Despite these noise effects, all damage cases tested on an experimental frame structure were detectable using the transfer entropy damage index.

Edge-reinforced random walk on a ladder

We prove that the edge-reinforced random walk on the ladder ℤ×{1,2} with initial weights a>3/4 is recurrent. The proof uses a known representation of the edge-reinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyze this Gibbsian process. Furthermore, we prove spatially exponentially fast decreasing bounds for normalized local times of the edge-reinforced random walk on a finite piece of the ladder, uniformly in the size of the finite piece.