Complete Causal Identification from Ancestral Graphs under Selection Bias

2026-03-27

AI Summary

This work addresses the open problem of complete causal effect identification from partial ancestral graphs (PAGs) in the presence of latent variables and selection bias. We establish, for the first time, an invariant set of extended conditional independence relations under PAGs and introduce a measure-theoretic formulation of do-calculus that accommodates selection bias. Building on these foundations, we derive necessary and sufficient conditions for causal identifiability within PAGs and present the first complete algorithm for causal identification in this setting, with formal proofs of its soundness and completeness. The proposed method effectively integrates observational and interventional data, incorporates background knowledge, and demonstrates broad applicability to complex causal discovery tasks.

Abstract

Many causal discovery algorithms, including the celebrated FCI algorithm, output a Partial Ancestral Graph (PAG). PAGs serve as an abstract graphical representation of the underlying causal structure, modeled by directed acyclic graphs with latent and selection variables. This paper develops a characterization of the set of extended-type conditional independence relations that are invariant across all causal models represented by a PAG. This theory allows us to formulate a general measure-theoretic version of Pearl's causal calculus and a sound and complete identification algorithm for PAGs under selection bias. Our results also apply when PAGs are learned by certain algorithms that integrate observational data with experimental data and incorporate background knowledge.

Problem

• causal identification
• ancestral graphs
• selection bias
• Partial Ancestral Graph
• causal discovery

Innovation

• causal identification
• ancestral graphs
• selection bias
• conditional independence
• causal calculus