Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects
This work addresses a practical challenge in causal inference for domains like public health by providing a more efficient and assumption-light method for CDE identification, though it is incremental as it builds on existing PC-style approaches.
The paper tackles the problem of identifying controlled direct effects (CDEs) when the underlying causal structure is unknown, by introducing a local essential graph (LEG) and algorithms (LocPC and LocPC-CDE) that recover it with fewer conditional independence tests and weaker assumptions than global methods, as demonstrated in simulation studies.
Understanding and identifying controlled direct effects (CDEs) is crucial across numerous scientific domains, including public health. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true underlying structure is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of $d$-separations, provide a more practical and realistic alternative. However, learning the full essential graph is computationally intensive and typically depends on strong, untestable assumptions. In this work, we characterize a local class of graphs, defined relative to a target variable, that share a specific subset of $d$-separations, and introduce a graphical representation of this class, called the local essential graph (LEG). We then present LocPC, a novel algorithm designed to recover the LEG from an observed distribution using only local conditional independence tests. Building on LocPC, we propose LocPC-CDE, an algorithm that discovers the portion of the LEG that is both sufficient and necessary to identify a CDE, bypassing the need of retrieving the full essential graph. Compared to global methods, our algorithms require less conditional independence tests and operate under weaker assumptions while maintaining theoretical guarantees. We illustrate the effectiveness of our approach through simulation studies.