  Several structure-learning algorithms for staged trees, asymmetric extensions
of Bayesian networks, have been proposed. However, these either do not scale
efficiently as the number of variables considered increases, a priori restrict
the set of models, or they do not find comparable models to existing methods.
Here, we define an alternative algorithm based on a totally ordered hyperstage.
We demonstrate how it can be used to obtain a quadratically-scaling structural
learning algorithm for staged trees that restricts the model space
a-posteriori. Through comparative analysis, we show that through the ordering
provided by the mean posterior distributions, we can outperform existing
methods in both computational time and model score. This method also enables us
to learn more complex relationships than existing model selection techniques by
expanding the model space and illustrates how this can embellish inferences in
a real study.
