Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex
This work addresses the challenge of efficiently estimating staged tree models for context-specific dependencies in Bayesian networks, representing an incremental improvement in computational efficiency for this specific domain.
The authors tackled the problem of estimating staged event tree models by proposing a hierarchical clustering framework on the probability simplex using various divergence metrics and linkage methods. Their results show that Total Variation divergence with Ward.D2 linkage achieves better model fit, structure recovery, and computational efficiency compared to alternatives like Backward Hill Climbing, which has higher computational costs.
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.