# Equivalence classes of staged trees

@article{Gorgen2018EquivalenceCO, title={Equivalence classes of staged trees}, author={Christiane Gorgen and Jim Q. Smith}, journal={Bernoulli}, year={2018} }

In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.

## 22 Citations

The curved exponential family of a staged tree

- MathematicsElectronic Journal of Statistics
- 2022

Abstract: 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…

An algebraic characterisation of staged trees : their geometry and causal implications

- Mathematics
- 2017

This dissertation develops the mathematical formalism to analyse now established staged tree models which are graphical, discrete and parametric statistical models. We investigate the properties of…

Discovery of statistical equivalence classes using computer algebra

- Computer Science, MathematicsInt. J. Approx. Reason.
- 2018

A new characterization of discrete decomposable models

- Computer Science
- 2021

This work provides a new characterization of perfect discrete DAG models in terms of their staged tree representations and identifies the family of balanced staged trees as the natural generalization of discrete decomposable models to the context-specific setting.

Staged trees are curved exponential families.

- Mathematics
- 2020

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…

Structural Learning of Simple Staged Trees

- Computer ScienceArXiv
- 2022

It is shown that data-learned simple staged trees often outperform Bayesian networks in model fit and how the coalesced graph is used to identify non-symmetric conditional independences is illustrated.

Constructing a Chain Event Graph from a Staged Tree

- Computer SciencePGM
- 2020

A simple iterative backward algorithm to obtain a CEG from any staged tree along with the functionality to add edges with sampling zeros and it is demonstrated that with an optimal stopping time, this algorithm is more efficient than the generalisation of a special case presented in Silander and Leong (2013).

A Differential Approach to Causality in Staged Trees

- Computer ScienceProbabilistic Graphical Models
- 2016

A recently developed differential approach to inference in staged tree models to causal inference finds that interventions on the model can be expressed as a very simple operation and can therefore clearly state causal hypotheses which are invariant for all staged trees representing the same causal model.

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