| This paper deals with the study of interacting systems networks. More precisely, we consider the problem of inferring the circulation of information between network nodes. To take into account feedback between signals, as well as instantaneous interaction, we show that the adequate measures of information flow are the directed information and the causal conditional directed information. We relate the framework based on directed information theory to the theory of Granger causality in multivariate time series. An important result of the paper is the proof that linear implementation of Granger causality and directed information theory are equivalent in the Gaussian case. This is proved for the bivariate analysis as well as for the multivariate analysis, for which we extend some of Geweke's results. The relations between directed information and transfer entropy are provided. A simulation illustrates the main results obtained in the paper through the problem of inferring effective connectivity in a network. |
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