Revisiting Madigan and Mosurski: Collapsibility via Minimal Separators

Abstract

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.