Revisiting Madigan and Mosurski: Collapsibility via Minimal Separators
本文重新审视列联表和图模型中的可折叠性，发现模型可折叠到目标集当且仅当该集包含非相邻顶点间的最小分隔子，并据此提出高效算法，使高维场景下的可折叠性分析变得可行。
Abstract Collapsibility provides a principled approach to dimension reduction in contingency tables and graphical models. Madigan & 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 on to a target set precisely when that set contains at least one minimal separator between its nonadjacent vertices. This insight motivates the close minimal separator absorption 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.