Unifying DAGs and UGs

TL;DR

This paper introduces a new class of graphical models that generalizes existing chain graphs by allowing more flexible edge configurations and relaxing acyclicity constraints, with proven Markov properties and causal interpretations.

Contribution

It proposes a novel class of graphical models that relaxes semi-directed acyclicity and allows multiple edges, extending the framework of chain graphs with proven properties.

Findings

Established local, pairwise, and global Markov properties for the new models.

Proved the equivalence of Markov properties and factorization.

Provided a causal interpretation of the models.

Abstract

We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed between any pair of nodes. Specifically, we present local, pairwise and global Markov properties for the new graphical models and prove their equivalence. We also present an equivalent factorization property. Finally, we present a causal interpretation of the new models.