• Corpus ID: 225103125

Staged trees are curved exponential families.

@article{Gorgen2020StagedTA,
  title={Staged trees are curved exponential families.},
  author={Christiane Gorgen and Manuele Leonelli and Orlando Marigliano},
  journal={arXiv: Statistics Theory},
  year={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 cumulant-generating function as functions of their graphical representation. We give necessary graphical criteria for classifying regular subfamilies and discuss implications for model selection. 
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References

SHOWING 1-10 OF 27 REFERENCES
Equivalence classes of staged trees
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
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
Stratified exponential families: Graphical models and model selection
We describe a hierarchy of exponential families which is useful for distinguishing types of graphical models. Undirected graphical models with no hidden variables are linear exponential families
Equations defining probability tree models
TLDR
It is found that the tree also provides a straightforward combinatorial tool to generalise the existing geometric characterisation of decomposable graphical models and Bayesian networks.
Bayesian MAP model selection of chain event graphs
TLDR
This paper demonstrates how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and proves that suitable homogeneity assumptions characterise the productDirichlet prior on this class of models.
Discovery of statistical equivalence classes using computer algebra
TLDR
A new algorithm exploits the primary decomposition of monomial ideals associated with an interpolating polynomials to quickly compute all nested representations of that polynomial, which determines an important subclass of all trees representing the same statistical model.
Causal discovery through MAP selection of stratified chain event graphs
We introduce a subclass of chain event graphs that we call stratified chain event graphs, and present a dynamic programming algorithm for the optimal selection of such chain event graphs that
A New Family of Non-Local Priors for Chain Event Graph Model Selection
Chain Event Graphs (CEGs) are a rich and provenly useful class of graphical models. The class contains discrete Bayesian Networks as a special case and is able to depict directly the asymmetric
A Dynamic Programming Algorithm for Learning Chain Event Graphs
TLDR
This paper describes a dynamic programming algorithm for exact learning of chain event graphs from multivariate data that allows reasonably fast approximations and provides clues for implementing more scalable heuristic algorithms.
Geometrical Foundations of Asymptotic Inference
Overview and Preliminaries. ONE-PARAMETER CURVED EXPONENTIAL FAMILIES. First-Order Asymptotics. Second-Order Asymptotics. MULTIPARAMETER CURVED EXPONENTIAL FAMILIES. Extensions of Results from the
...
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