# Learning Staged Trees from Incomplete Data

arXiv: https://arxiv.org/abs/2405.18306 · HTML: https://mlsanity.com/paper/2405.18306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 16 of 16)

- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [The R Package stagedtrees for Structural Learning of Stratified Staged Trees](https://mlsanity.com/paper/2004.06459/) (2020)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [The curved exponential family of a staged tree](https://mlsanity.com/paper/2010.15515/) (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)
- [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)
- [Hard and Soft EM in Bayesian Network Learning from Incomplete Data](https://mlsanity.com/paper/2012.05269/) (2020)
- [Learning Bayesian Networks from Incomplete Data with the Node-Average Likelihood](https://mlsanity.com/paper/2004.14441/) (2020)
- [cegpy: Modelling with Chain Event Graphs in Python](https://mlsanity.com/paper/2211.11366/) (2022)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [Staged trees for discrete longitudinal data](https://mlsanity.com/paper/2401.04297/) (2024)
- [On the closure of relational models](https://mlsanity.com/paper/1501.00600/) (2015)
- [Hierarchical Aitchison-Silvey models for incomplete binary sample spaces](https://mlsanity.com/paper/2002.00357/) (2020)
- [Score Equivalence for Staged Trees](https://mlsanity.com/paper/2206.15322/) (2022)

## Built on by (most cited first, 1 of 1)

- [Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex](https://mlsanity.com/paper/2603.15568/) (2026)

## Abstract (arXiv)

Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees from data, under the frequentist or Bayesian paradigm. They assume a data set has been observed fully and, in practice, observations with missing entries are either dropped or imputed before learning the model. Here, we introduce the first algorithms for staged trees that handle missingness within the learning of the model. To this end, we characterize the likelihood of staged tree models in the presence of missing data and discuss pseudo-likelihoods that approximate it. A structural expectation-maximization algorithm estimating the model directly from the full likelihood is also implemented and evaluated. A computational experiment showcases the performance of the novel learning algorithms, demonstrating that it is feasible to account for different missingness patterns when learning staged trees.