arXiv 2510.090242025-10stat.ME

重新审视Madigan和Mosurski：通过最小分隔符实现可压缩性

Revisiting Madigan and Mosurski: Collapsibility via Minimal Separators

KLAS and School of Mathematics and Statistics, Northeast Normal University（东北师范大学数学与统计学院）；The Academy for Advanced Interdisciplinary Studies, Beijing Key Laboratory of Applied Statistics and Digital Regulation, School of Mathematics and Statistics, Beijing Technology and Business University（北京工商大学数学与统计学院）；Institute of Statistics and Data Science, Xinjiang University of Finance and Economics（新疆财经大学统计与数据科学学院）

Pei Heng, Shiyuan He, Yi Sun, Jianhua Guo

备注：: 8 pages, 2 figures, Code available at https://github.com/Balance-H/Algorithms
发表信息：: Biometrika, Volume 113, Issue 3, 2026, asag024
DOI：: 10.1093/biomet/asag024

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AI总结：

研究可压缩性在列联表和图形模型中降维的方法。利用最小分隔符的见解推动CMSA算法，以低成本构建最小可压缩集，模拟证实该算法在高维设置中效率大幅提升。

摘要：

可压缩性为列联表和图形模型中的降维提供了一种有原则的方法。Madigan和Mosurski（1990）开创了可分解模型中最小可压缩集的研究，但通用图的现有算法计算要求仍然很高。我们表明，当目标集包含其非相邻顶点之间的至少一个最小分隔符时，模型恰好可压缩到该目标集上。这一见解推动了紧密最小分隔符吸收（CMSA）算法的发展，该算法仅使用局部分隔符搜索以非常低的成本构建最小可压缩集。模拟证实了效率的大幅提高，使得可压缩性分析在高维设置中切实可行。

英文摘要：

Collapsibility provides a principled approach for dimension reduction in contingency tables and graphical models. Madigan and Mosurski (1990) pioneered the study of minimal collapsible sets in decomposable models, but existing algorithms for general graphs remain computationally demanding. We show that a model is collapsible onto a target set precisely when that set contains at least one minimal separator between its non-adjacent vertices. This insight motivates the Close Minimal Separator Absorption (CMSA) algorithm, which constructs minimal collapsible sets using only local separator searches at very low costs. Simulations confirm substantial efficiency gains, making collapsibility analysis practical in high-dimensional settings.

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