Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex

2026-03-16

AI Summary

This study addresses staged event tree models with context-specific dependence structures by proposing an efficient modeling approach based on hierarchical clustering over the probability simplex. Through a systematic evaluation of various combinations of divergence measures—including total variation, Hellinger, Fisher, and Kaniadakis—and linkage strategies such as Ward.D2, average, complete, and McQuitty, the work demonstrates for the first time that the pairing of total variation divergence with Ward.D2 linkage consistently outperforms the conventional Backward Hill Climbing method. This combination achieves superior performance in terms of model fit accuracy, ability to recover the true underlying structure, and computational efficiency, thereby offering an improved solution for constructing staged event trees.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Ensemble Methods
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• staged event tree
• model estimation
• computational efficiency
• structure recovery
• probability simplex

Innovation

• staged tree models
• hierarchical clustering
• probability simplex
• Total Variation divergence
• Ward.D2 linkage