Equivalence between minimal generative model graphs and directed information graphs

We propose a new type of probabilistic graphical model, based on directed information, to represent the causal dynamics between processes in a stochastic system. We show the practical significance of such graphs by proving their equivalence to generative model graphs which succinctly summarize interdependencies for causal dynamical systems under mild assumptions. This equivalence means that directed information graphs may be used for causal inference and learning tasks in the same manner Bayesian networks are used for correlative statistical inference and learning.