# Structural Learning of Simple Staged Trees

arXiv: https://arxiv.org/abs/2203.04390 · HTML: https://mlsanity.com/paper/2203.04390/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 8 Mar 2022.

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

- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (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)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [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)
- [Constructing a Chain Event Graph from a Staged Tree](https://mlsanity.com/paper/2006.15857/) (2020)
- [A Separation Theorem for Chain Event Graphs](https://mlsanity.com/paper/1501.05215/) (2015)
- [Equivalence Classes of Staged Trees](https://mlsanity.com/paper/1512.00209/) (2015)

## Built on by (most cited first, 7 of 7)

- [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)
- [Integrating Probabilistic Trees and Causal Networks for Clinical and Epidemiological Data](https://mlsanity.com/paper/2501.15973/) (2025)
- [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 faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents non-symmetric conditional independences via vertex coloring. However, since they are based on a tree representation of the sample space, the underlying graph becomes cluttered and difficult to visualize as the number of variables increases. Here we introduce the first structural learning algorithms for the class of simple staged trees, entertaining a compact coalescence of the underlying tree from which non-symmetric independences can be easily read. We show that data-learned simple staged trees often outperform Bayesian networks in model fit and illustrate how the coalesced graph is used to identify non-symmetric conditional independences.