Staged trees and asymmetry-labeled DAGs

Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they can be seen as a special case of the much more general class of models called staged trees, which can represent any non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of a staged tree, which can be used to read conditional independences intuitively. A new labeled graph termed asymmetry-labeled directed acyclic graph is defined, with edges labeled to denote the type of dependence between any two random variables. We also present a novel algorithm to learn staged trees which only enforces a specific subset of non-symmetric independences. Various datasets illustrate the methodology, highlighting the need to construct models that more flexibly encode and represent non-symmetric structures.