Title: Marginalized local independence graphs
Authors: Soeren Wengel Mogensen - University of Copenhagen (Denmark) [presenting]
Niels Richard Hansen - University of Copenhagen (Denmark)
Abstract: Local independence is an asymmetric notion of independence which describes how a system of stochastic processes evolves over time. Let $A$, $B$, and $C$ be three subsets of the coordinate processes of the stochastic system. Intuitively speaking, $B$ is locally independent of $A$ given $C$ if at every point in time knowing the past of both $A$ and $C$ is not more informative about the present of $B$ than knowing the past of $C$ only. Previous work has used directed graphs equipped with $\delta$-separation for graphical representation of local independence structures. In such local independence graphs each node corresponds to an entire coordinate process rather than to a single random variable. We consider marginalization of local independence graphs and introduce a class of graphs which describe partially observed local independence models. We also introduce $\mu$-separation, a generalization of $\delta$-separation. This class of graphs satisfies a central maximality property which allows one to construct a simple graphical representation of an entire Markov equivalence class of marginalized local independence graphs. This is convenient as the equivalence class can be learned from data and its graphical representation concisely describes what underlying structure could have generated the observed local independencies.