Identifying Conditional Causal Effects in MPDAGs
This work addresses a fundamental challenge in causal inference for researchers and practitioners dealing with partial knowledge of causal structures, offering incremental advancements in methodology for this specific domain.
The paper tackles the problem of identifying conditional causal effects when the causal graph is only known up to a maximally oriented partially directed acyclic graph (MPDAG), providing an identification formula for cases where the conditioning set is unaffected by treatment, a generalization of do calculus to MPDAGs, and a complete algorithm for this task.
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.