# Staged trees and asymmetry-labeled DAGs

arXiv: https://arxiv.org/abs/2108.01994 · HTML: https://mlsanity.com/paper/2108.01994/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 62 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 17 of 17)

- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Bayesian Networks in Healthcare: Distribution by Medical Condition](https://mlsanity.com/paper/2002.00224/) (2020)
- [The R Package stagedtrees for Structural Learning of Stratified Staged Trees](https://mlsanity.com/paper/2004.06459/) (2020)
- [A Bayesian Approach to Learning Bayesian Networks with Local Structure](https://mlsanity.com/paper/1302.1528/) (2013)
- [Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models](https://mlsanity.com/paper/1310.1187/) (2013)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Learning Bayesian Networks with Local Structure](https://mlsanity.com/paper/1302.3577/) (2013)
- [The curved exponential family of a staged tree](https://mlsanity.com/paper/2010.15515/) (2020)
- [A New Perspective on Learning Context-Specific Independence](https://mlsanity.com/paper/2006.06896/) (2020)
- [Algorithms for Causal Reasoning in Probability Trees](https://mlsanity.com/paper/2010.12237/) (2020)
- [Sensitivity analysis beyond linearity](https://mlsanity.com/paper/1901.02062/) (2018)
- [A new class of generative classifiers based on staged tree models](https://mlsanity.com/paper/2012.13798/) (2020)
- [Algebraic geometry of discrete interventional models](https://mlsanity.com/paper/2012.03593/) (2020)
- [Model-Preserving Sensitivity Analysis for Families of Gaussian Distributions](https://mlsanity.com/paper/1809.10794/) (2018)
- [Context-specific independence in graphical log-linear models](https://mlsanity.com/paper/1409.2713/) (2014)
- [A Separation Theorem for Chain Event Graphs](https://mlsanity.com/paper/1501.05215/) (2015)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)

## Built on by (most cited first, 8 of 8)

- [Structural Learning of Simple Staged Trees](https://mlsanity.com/paper/2203.04390/) (2022)
- [Highly Efficient Structural Learning of Sparse Staged Trees](https://mlsanity.com/paper/2206.06970/) (2022)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [Learning Staged Trees from Incomplete Data](https://mlsanity.com/paper/2405.18306/) (2024)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)
- [Context-Specific Refinements of Bayesian Network Classifiers](https://mlsanity.com/paper/2405.18298/) (2024)
- [Staged Event Trees for Transparent Treatment Effect Estimation](https://mlsanity.com/paper/2509.26265/) (2025)
- [Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex](https://mlsanity.com/paper/2603.15568/) (2026)

## Abstract (arXiv)

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.