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

TL;DR

This paper introduces a scalable algorithm for staged tree model selection that leverages mean-posterior clustering, outperforming existing methods in efficiency and complexity, and enabling richer inferences.

Contribution

It proposes a new quadratically-scaling structure-learning algorithm for staged trees based on totally ordered hyperstages, expanding the model space a-posteriori.

Findings

Outperforms existing methods in computational time

Achieves higher model scores in comparative analysis

Enables learning more complex relationships

Abstract

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.