Conditional local independence, or Granger non-causality, is a notion of conditional independence among coordinates of a multivariate stochastic process. Local independence graphs can be used to encode such conditional local independencies, and the abstract and asymmetric independence models encoded by directed, and possibly cyclic graphs, are of intrinsic interest.
In the talk I will introduce conditional local independence and local independence graphs via a classical example of a time homogeneous multivariate Markov process with binary coordinates. This will illustrate how local independence graphs relate to classical graphical models, such as the Ising model, but also how they generalize such
models by allowing for an asymmetric dependence over time. I will then show some of the main results we know about local independence graphs, such as marginalization operations and a characterization of Markov equivalence classes, and I will outline how local independence graphs can be learned via conditional local independence testing.