Staged trees and asymmetry-labeled DAGs
This work addresses the limitation of Bayesian networks in handling non-symmetric structures for researchers in probabilistic graphical models, though it appears incremental as it builds on existing staged tree theory.
The paper tackles the problem of representing non-symmetric conditional independence in probabilistic models by formalizing the relationship between Bayesian networks and staged trees, introducing a minimal Bayesian network representation and a new asymmetry-labeled DAG. It presents a novel algorithm for learning staged trees and illustrates the methodology on various datasets, highlighting the need for more flexible models.
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 type of non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of the staged tree, which can be used to read conditional independences in an intutitive way. A new labeled graph termed asymmetry-labeled directed acyclic graph is defined, whose edges are labeled to denote the type of dependence existing 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 are used to illustrate the methodology, highlighting the need to construct models which more flexibly encode and represent non-symmetric structures.