Scalable Model Selection for Staged Trees: Mean-posterior Clustering and Binary Trees

Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these do not scale efficiently as the number of variables considered increases, a priori restricting 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 computational time whilst providing comparable model scores. This method also enables us to learn more complex relationships than existing model selection techniques by expanding the model space. We illustrate how this can embellish inferences in a real study.