This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework. Finally, experiments and empirical analysis show the effectiveness of the collapsibility for causal estimations in CPDAGs. Code is available at https://github.com/Jamyang-D/strongly-convex.

翻译：本文提出了一种用于估计因果效应的可压缩方法，该方法在完全部分有向无环图（CPDAGs）中对某些变量进行边缘化前后保持估计量的一致性。我们首先引入CPDAGs的估计可压缩性，并将最小可压缩集刻画为强d-凸包。我们设计了一种高效算法来获取DAGs中的此类集合，并将其推广到CPDAGs。随后，我们将图约简过程与IDA框架相结合。最后，实验与实证分析展示了可压缩性在CPDAGs因果估计中的有效性。代码可在 https://github.com/Jamyang-D/strongly-convex 获取。