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

2026-06-08 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

This paper introduces a collapsible method for estimating causal effects, specifically designed to maintain estimator consistency both before and after marginalization over certain variables within completed partially directed acyclic graphs (CPDAGs). The research formally defines estimate collapsibility for CPDAGs and characterizes the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is developed to obtain such sets in DAGs, which is then generalized for broader application in CPDAGs. The proposed approach further integrates a graph reduction procedure with the IDA framework. Empirical analysis and experiments demonstrate the effectiveness of this collapsibility for improving causal estimations in CPDAGs, with code available at https://github.com/Jamyang-D/strongly-convex.

Key takeaway

For research scientists and data scientists working with causal inference in complex systems, this method offers a way to ensure the consistency of your causal effect estimates when marginalizing over variables in CPDAGs. You should consider implementing the proposed algorithm for identifying strong d-convex hulls and integrating the graph reduction procedure with your IDA framework to improve the reliability of your causal models.

Key insights

A collapsible method estimates causal effects in CPDAGs, maintaining consistency before and after marginalization.

Principles

• Estimate collapsibility ensures consistency across marginalization.
• Minimal collapsible sets are strong d-convex hulls.

Method

Devises an efficient algorithm to find strong d-convex hulls in DAGs, generalizes it to CPDAGs, and combines graph reduction with the IDA framework.

In practice

• Apply the algorithm to identify minimal collapsible sets.
• Integrate graph reduction with IDA for robust causal estimation.

Topics

• Causal Effects
• CPDAGs
• d-Convex Hulls
• Graph Reduction
• IDA Framework
• Machine Learning

Code references

• Jamyang-D/strongly-convex

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.