# The curved exponential family of a staged tree

arXiv: https://arxiv.org/abs/2010.15515 · HTML: https://mlsanity.com/paper/2010.15515/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [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)
- [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)

Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their graphical representation. We give necessary and sufficient graphical criteria for classifying regular subfamilies and discuss implications for model selection.