用单纯形聚类提升阶段树模型估计效率，更快更准。
Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex
- 在概率单纯形上用层次聚类估计阶段树结构
- 总变差距离+Ward.D2链接效果最佳，拟合优度和结构恢复好
- 相比传统方法计算快得多，适合大规模场景
阶段树模型通过基于阶段的结构引入上下文相关依赖，拓展了贝叶斯网络。本文提出一种新框架，利用单纯形上的层次聚类与基于单纯形的差异度量来估计阶段树。我们系统评估了多种距离与发散度量（总变差、赫林格、费舍尔、卡尼亚达基斯）及链接方法（Ward.D2、平均、完全、McQuitty）。仿真实验表明，总变差距离结合Ward.D2链接在模型拟合、结构恢复和计算效率方面均表现最优。使用相对贝叶斯信息准则（BIC）和汉明距离评估性能，结果表明尽管反向爬山法（BHC）表现接近，但其计算成本显著更高；而总变差+Ward.D2在性能相当的情况下实现更优的计算效率，更适合大规模或实时任务。
原文摘要 · Abstract (English)
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.
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