The influence of filtering and downsampling on the estimation of transfer entropy.

Immo Weber,Lars Timmermann,Michael Von Papen,Esther Florin,Jun Ma

doi:10.1371/journal.pone.0188210

Abstract

Transfer entropy (TE) provides a generalized and model-free framework to study Wiener-Granger causality between brain regions. Because of its nonparametric character, TE can infer directed information flow also from nonlinear systems. Despite its increasing number of applications in neuroscience, not much is known regarding the influence of common electrophysiological preprocessing on its estimation. We test the influence of filtering and downsampling on a recently proposed nearest neighborhood based TE estimator. Different filter settings and downsampling factors were tested in a simulation framework using a model with a linear coupling function and two nonlinear models with sigmoid and logistic coupling functions. For nonlinear coupling and progressively lower low-pass filter cut-off frequencies up to 72% false negative direct connections and up to 26% false positive connections were identified. In contrast, for the linear model, a monotonic increase was only observed for missed indirect connections (up to 86%). High-pass filtering (1 Hz, 2 Hz) had no impact on TE estimation. After low-pass filtering interaction delays were significantly underestimated. Downsampling the data by a factor greater than the assumed interaction delay erased most of the transmitted information and thus led to a very high percentage (67–100%) of false negative direct connections. Low-pass filtering increases the number of missed connections depending on the filters cut-off frequency. Downsampling should only be done if the sampling factor is smaller than the smallest assumed interaction delay of the analyzed network.

Highlights

Understanding the connectivity and directional interaction of different brain areas is highly relevant in order to gain further insight into brain function
For the control and all filtered data sets false negative direct connections (FNDC) and false positive connections (FP) were detected to be below five percent
For false negative indirect connections (FNIC) filtering with progressively lower low-pass cut-off frequencies led to a significant monotonic increase from 27% for the control group up to 86% for the 80 Hz low-pass filter

Summary

Introduction

Understanding the connectivity and directional interaction of different brain areas is highly relevant in order to gain further insight into brain function. In electrophysiological research Granger causality [1] and its multivariate extensions such as partial directed coherence [2], have been applied for this aim, resulting in extensive progress in understanding information flow in the healthy [3,4,5,6] and pathological brain alike [7,8,9,10,11]. One disadvantage of classical Granger causality is the need for a linear autoregressive model. Granger causality cannot always properly identify nonlinear interactions.

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