Constructing a Chain Event Graph from a Staged Tree

Aditi Shenvi; Jim Q. Smith

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arXiv · 2006.15857

Constructing a Chain Event Graph from a Staged Tree

Aditi Shenvi·Jim Q. Smith

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Abstract

Chain Event Graphs (CEGs) are a recent family of probabilistic graphical models - a generalisation of Bayesian Networks - providing an explicit representation of structural zeros, structural missing values and context-specific conditional independences within their graph topology. A CEG is constructed from an event tree through a sequence of transformations beginning with the colouring of the vertices of the event tree to identify one-step transition symmetries. This coloured event tree, also known as a staged tree, is the output of the learning algorithms used for this family. Surprisingly, no general algorithm has yet been devised that automatically transforms any staged tree into a CEG representation. In this paper we provide a simple iterative backward algorithm for this transformation. Additionally, we show that no information is lost from transforming a staged tree into a CEG. Finally, we demonstrate that with an optimal stopping criterion, our algorithm is more efficient than the generalisation of a special case presented in Silander and Leong (2013). We also provide Python code using this algorithm to obtain a CEG from any staged tree along with the functionality to add edges with sampling zeros.

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Aditi Shenvi, Jim Q. Smith. 2021-12-16. Constructing a Chain Event Graph from a Staged Tree. https://arxiv.org/abs/2006.15857

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