Rényi information transfer: Partial rényi transfer entropy and partial rényi mutual information

Shannon and Rényi information theory have been applied to coupling estimation in complex systems using time series of their dynamical states. By analysing how information is transferred between constituent parts of a complex system, it is possible to infer the coupling parameters of the system. To this end, we introduce the partial Rényi transfer entropy and we give an alternative derivation of the partial Rényi mutual information, using the conditional Rényi α-divergence. We prove that, in the limit α → 1, this divergence tends to the conditional Kullback-Leibler divergence from Shannon information theory. As a result, when α → 1, we obtain the partial transfer entropy and the partial mutual information from their Rényi equivalents. Using these Rényi information-theoretic functionals, we identify the coupling direction and delay between two processes in an autoregressive system of order 1.