Staged trees and asymmetry-labeled DAGs

TL;DR

This paper explores the relationship between staged trees and Bayesian networks, introducing asymmetry-labeled DAGs and a new algorithm for learning staged trees that better capture non-symmetric dependencies.

Contribution

It formalizes the connection between staged trees and Bayesian networks, introduces asymmetry-labeled DAGs, and proposes a novel algorithm for learning staged trees with selective non-symmetric independences.

Findings

Asymmetry-labeled DAGs effectively encode non-symmetric dependencies.

The new algorithm improves modeling of non-symmetric structures.

Empirical results demonstrate the flexibility of the proposed models.

Abstract

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.