Measuring causal relationships in dynamical systems through recovery of functional dependencies

We introduce a measure of causality that captures the functional dependencies in dynamical systems and subsequently, define a new type of graphical model, functional dependency graph, to encode such dependencies. We study the relationship between this type of graphical model and other graphical models such as directed information graphs and linear dynamical graphs that have been proposed to capture causal influences in dynamical systems. We show that functional dependency graphs are a generalization of these previously introduced graphical models and learn the functional dependencies in a larger class of models. We also establish sufficient conditions under which the functional dependency graph defined through our measure is equivalent to the directed information graphs. Some simulation results on linear and nonlinear dynamics are provided.