Identifying Conditional Causal Effects in MPDAGs

TL;DR

This paper develops methods for identifying conditional causal effects in MPDAGs, which encode causal structures with partial orientation and background knowledge, providing formulas, a generalized do calculus, and a complete algorithm.

Contribution

It introduces a novel framework for conditional effect identification in MPDAGs, including formulas, a generalized do calculus, and a complete algorithm.

Findings

Provided an identification formula for unaffected conditioning sets.

Generalized do calculus for MPDAGs.

Developed a complete algorithm for conditional effect identification.

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.