Equivalence Classes of Staged Trees

TL;DR

This paper characterizes the statistical equivalence classes of staged trees and CEGs, showing they share a polynomial description and can be transformed through simple polynomial operations, with applications to real data analysis.

Contribution

It provides a complete characterization of equivalence classes of staged trees and CEGs using polynomial descriptions and transformation methods.

Findings

All graphical representations of the same model share a common polynomial description.

Transformations on the polynomial enable traversal of equivalence classes.

Application to real data illustrates the method's practical utility.

Abstract

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 common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.