Estimate Collapsibility of Causal Effects in Completed Partial DAGs via Strong d-Convex Hulls

2026-06-07

AI Summary

This work addresses the bias in causal effect estimation that arises when marginalizing variables in partially observable causal graphs represented as completed partially directed acyclic graphs (CPDAGs). The authors formally define estimand collapsibility within CPDAGs for the first time and introduce the notion of a “strong d-convex hull” to characterize minimal collapsible sets. Building on this characterization, they develop an efficient algorithm that integrates graph reduction techniques with the Intervention calculus when the DAG is Absent (IDA) framework to achieve consistent causal effect estimation. Theoretical analysis and empirical experiments demonstrate that the proposed method substantially outperforms existing approaches in preserving estimation consistency, and the implementation has been made publicly available.

Abstract

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.

Problem

• collapsibility
• causal effects
• CPDAGs
• d-convex hulls
• marginalization

Innovation

• estimate collapsibility
• strong d-convex hull
• CPDAG
• causal effect estimation
• graph reduction