Unifying DAGs and UGs
This work provides a theoretical extension for graphical models, which is incremental and primarily relevant for researchers in probabilistic graphical models and causality.
The authors tackled the problem of generalizing chain graphs by relaxing the semi-directed acyclity constraint to allow only directed cycles and up to two edges between nodes, resulting in a new class of graphical models with proven equivalence of Markov properties and an equivalent factorization property.
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.