The curved exponential family of a staged tree. (English) Zbl 1493.62416

Summary: 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.


62H99 Multivariate analysis
68T99 Artificial intelligence


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