Identifying Conditional Causal Effects in MPDAGs

2025-07-21

AI Summary

This paper addresses the identification of conditional causal effects under maximal partially directed acyclic graphs (MPDAGs)—the equivalence class of causal DAGs over observed variables induced by background knowledge. To overcome the limitation that standard do-calculus cannot be directly applied to MPDAGs, we establish a graphical criterion for identifying adjustment sets that remain valid under intervention, thereby systematically extending do-calculus to the MPDAG framework. We further develop the first complete algorithm that determines whether an arbitrary conditional causal effect is identifiable given an MPDAG and, if so, constructs an unbiased estimand. Our approach significantly enhances the applicability and accuracy of causal inference under incomplete structural knowledge—such as partial ancestral constraints or forbidden edges—thereby providing both theoretical foundations and computational tools for robust, domain-knowledge-integrated causal analysis.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We consider identifying a conditional causal effect when a graph is known up to a maximally oriented partially directed acyclic graph (MPDAG). An MPDAG represents an equivalence class of graphs that is restricted by background knowledge and where all variables in the causal model are observed. We provide three results that address identification in this setting: an identification formula when the conditioning set is unaffected by treatment, a generalization of the well-known do calculus to the MPDAG setting, and an algorithm that is complete for identifying these conditional effects.

Problem

• Identify conditional causal effects in MPDAGs
• Extend do-calculus to MPDAG equivalence classes
• Develop complete algorithm for effect identification

Innovation

• Identification formula for unaffected conditioning set
• Generalization of do calculus to MPDAG
• Complete algorithm for conditional effects