Complete Causal Identification from Ancestral Graphs under Selection Bias

TL;DR

This paper introduces a comprehensive method for causal identification from PAGs under selection bias, extending causal calculus and providing a complete algorithm applicable to various data integration scenarios.

Contribution

It develops a measure-theoretic framework and a sound, complete identification algorithm for PAGs under selection bias, enhancing causal discovery methods.

Findings

Characterization of invariant conditional independence relations across PAGs.

A measure-theoretic version of Pearl's causal calculus.

A sound and complete identification algorithm for PAGs under selection bias.

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.