| Causality is a broad concept that can be understood in many ways. A popular and conceptually simple approach is the so-called Granger causality, which leans on the idea that the cause occurs before the effect and, therefore, knowledge of the cause helps forecasting the effect. Determining whether a system Granger causes another one is a problem addressed in disciplines as diverse as climatology, economics, chaotic communication and the neurosciences. When a model of the underlying motion dynamics is not available, a sound information-theoretic approach to measure Granger-causality is the transfer entropy. However, TE is able to identify only pairwise interactions, which is a major limiting factor when analyzing networks of many dynamical nodes like those often found in brain research. Recently, partial mutual information (PMI) has been proposed as a multivariate alternative to the TE. In this talk we introduce the concept of multivariate transfer entropy (MTE) and we show that MTE and PMI are complementary measures, which offer slightly different views of the underlying connectivity. Subsequently, we propose an MTE estimator specially suited for the analysis of ensembles of repeated measurements with (possibly) time-varying underlying connectivity. |
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