Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex

TL;DR

This paper introduces a novel method for estimating staged event tree models using hierarchical clustering on the probability simplex, demonstrating improved efficiency and model quality over existing approaches.

Contribution

The study proposes a new framework employing simplex-based divergences and hierarchical clustering for staged tree estimation, with extensive evaluation of divergence metrics and linkage methods.

Findings

Total Variation with Ward.D2 linkage yields better model fit and efficiency.

BHC provides competitive results but is more computationally intensive.

Total Variation divergence offers a good balance of performance and speed.

Abstract

Staged tree models enhance Bayesian networks by incorporating context-specific dependencies through a stage-based structure. In this study, we present a new framework for estimating staged trees using hierarchical clustering on the probability simplex, utilizing simplex basesd divergences. We conduct a thorough evaluation of several distance and divergence metrics including Total Variation, Hellinger, Fisher, and Kaniadakis; alongside various linkage methods such as Ward.D2, average, complete, and McQuitty. We conducted the simulation experiments that reveals Total Variation, especially when combined with Ward.D2 linkage, consistently produces staged trees with better model fit, structure recovery, and computational efficiency. We assess performance by utilizing relative Bayesian Information Criterion (BIC), and Hamming distance. Our findings indicate that although Backward Hill Climbing (BHC) delivers competitive outcomes, it incurs a significantly higher computational cost. On the other, Total Variation divergence with Ward.D2 linkage, achieves similar performance while providing significantly better computational efficiency, making it a more viable option for large-scale or time sensitive tasks.