Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects

TL;DR

This paper introduces LocPC and LocPC-CDE algorithms that efficiently identify causal effects by focusing on local graph structures, reducing computational complexity and assumptions compared to traditional global methods.

Contribution

The paper proposes the local essential graph (LEG) and algorithms LocPC and LocPC-CDE for targeted causal discovery, improving efficiency and weakening assumptions in identifying controlled direct effects.

Findings

LocPC requires fewer conditional independence tests than global methods.

LocPC-CDE accurately identifies necessary graph portions for CDEs.

Algorithms operate under weaker assumptions with theoretical guarantees.

Abstract

Identifying controlled direct effects (CDEs) is crucial across numerous scientific domains. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true DAG is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of conditional independencies, provide a more practical and realistic alternative, and the PC algorithm is one of the most widely used method to learn them using conditional independence tests. However, learning the full essential graph is computationally intensive and relies on strong, untestable assumptions. In this work, we adapt the PC algorithm to recover only the portion of the graph needed for identifying CDEs. In particular, we introduce the local essential graph (LEG), a graph structure defined relative to a target variable, and present LocPC, an algorithm that learns the LEG using solely local conditional independence tests. Building on this, we develop LocPC-CDE, which extracts precisely the portion of the LEG that is both necessary and sufficient for identifying a CDE. 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 on synthetic and real data.