Constructing a Chain Event Graph from a Staged Tree

TL;DR

This paper introduces a simple iterative backward algorithm to transform staged trees into Chain Event Graphs (CEGs), ensuring no information loss and improving efficiency over previous methods, with practical Python implementation provided.

Contribution

The paper presents the first general algorithm for converting any staged tree into a CEG, enhancing the modeling of complex probabilistic structures.

Findings

The algorithm guarantees no information loss during transformation.

It is more efficient than previous methods with an optimal stopping criterion.

Python code implementation is provided for practical use.

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.