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Applied Network Science
Fig. 2 | Applied Network Science

Fig. 2

From: Interaction networks from discrete event data by Poisson multivariate mutual information estimation and information flow with applications from gene expression data

Fig. 2

a The causation entropy between two processes Z and Y is shown. In this case since we are only conditioning on a process X, \(C_{Z \rightarrow Y\mid X} = T_{Z \rightarrow Y}\). Of course X may be replaced with a set of variables. b Here we show a special case where Z is independent of both X and Y (Z in this case may represent the history of X. In this case it becomes clear that \(H(Z\mid X,Y) = H(Z)\), \(H(X\mid Y,Z) = H(X\mid Y)\) and \(H(Y\mid X,Z) = H(Y\mid X)\). As explained in the text, this special case helps us to discern what are the proper variables to use in the Poisson case

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