Constructing a Chain Event Graph from a Staged Tree
This work addresses a gap in probabilistic graphical modeling for researchers and practitioners, offering an incremental improvement in algorithm efficiency for constructing CEGs from staged trees.
The paper tackles the problem of automatically transforming any staged tree into a Chain Event Graph (CEG) representation, providing a simple iterative backward algorithm that is more efficient than prior methods with an optimal stopping criterion.
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.