Partial mutual information for coupling analysis of multivariate time series

We propose a method to discover couplings in multivariate time series, based on partial mutual information, an information-theoretic generalization of partial correlation. It represents the part of mutual information of two random quantities that is not contained in a third one. By suitable choice of the latter, we can differentiate between direct and indirect interactions and derive an appropriate graphical model. An efficient estimator for partial mutual information is presented as well.