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. 
View PDF on arXiv
22 Citations
Highly Influential Citations
1
Background Citations
7
Methods Citations
10
Results Citations
1

Figures from this paper

22 Citations

Citation Type

Citation Type

The curved exponential family of a staged tree
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
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
A new characterization of discrete decomposable models
TLDR
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.
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
TLDR
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.
Equations defining probability tree models
Staged tree models with toric structure
Constructing a Chain Event Graph from a Staged Tree
TLDR
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
TLDR
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.
...
1
2
3
...

References

SHOWING 1-10 OF 41 REFERENCES
An algebraic characterisation of staged trees : their geometry and causal implications
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…
A Differential Approach for Staged Trees
TLDR
This paper formalises a symbolic approach for staged trees, a model class making it possible to visualise asymmetric model constraints, and shows that the probability parametrisation associated to trees has several advantages over the one associated to Bayesian networks.
On the toric algebra of graphical models
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general…
A characterization of Markov equivalence classes for acyclic digraphs
Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In…
A Separation Theorem for Chain Event Graphs
TLDR
This paper introduces a separation theorem for CEGs, analogous to the d-separation theorem for BNs, which likewise allows an analyst to identify the conditional independence structure of their model from the topology of the graph.
A Differential Approach to Causality in Staged Trees
TLDR
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.
Conditional independence and chain event graphs
Causal analysis with Chain Event Graphs
Causal discovery through MAP selection of stratified chain event graphs
TLDR
A dynamic programming algorithm is presented for the optimal selection of such chain event graphs that maximizes a decomposable score derived from a complete independent sample and it is shown that the algorithm is suitable for small problems.
Bayesian MAP model selection of chain event graphs
...
1
2
3
4
5
...