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<p>A graphical model is said to be collapsible onto a subset if the implied model for the marginal distributions over the subset is equal to the model given by the related induced subgraph. In this paper, we extend the concepts of t-removable and c-removable vertices, proposed by Xie and Geng (<CitationRef CitationID="CR35">2009</CitationRef>), to t-removable and c-removable sets in terms of inducing paths. We show that, under certain conditions, these extensions are equivalent, respectively, to model collapsibility and estimate collapsibility for directed graphical models. We provide polynomial time algorithms with respect to the number of variables to determine whether a given set of variables is removable. The code for this study is available at <a href="https://github.com/Jamyang-D/removable-sets-check">https://github.com/Jamyang-D/removable-sets-check</a>.</p>

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Identifying Collapsible Sets in Directed Graphical Models via Inducing Paths

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Yuxin Deng,
  • Yi Sun,
  • Huaxiong Liu

摘要

A graphical model is said to be collapsible onto a subset if the implied model for the marginal distributions over the subset is equal to the model given by the related induced subgraph. In this paper, we extend the concepts of t-removable and c-removable vertices, proposed by Xie and Geng (2009), to t-removable and c-removable sets in terms of inducing paths. We show that, under certain conditions, these extensions are equivalent, respectively, to model collapsibility and estimate collapsibility for directed graphical models. We provide polynomial time algorithms with respect to the number of variables to determine whether a given set of variables is removable. The code for this study is available at https://github.com/Jamyang-D/removable-sets-check.