Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects
Published on: October 23, 2023
Source: arXiv:2505.02781v4
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. The PC algorithm is one of the most widely used methods to learn them using conditional independence tests. However, learning the full essential graph is computationally intensive and relies on strong, untestable assumptions.
Introduction
In the field of causal inference, identifying controlled direct effects is a foundational task that has significant implications in various scientific disciplines. Traditional methods typically operate on the premise of known causal structures, often represented as directed acyclic graphs (DAGs). However, in real-world applications, these assumptions may not hold, leading researchers to seek alternative methodologies.
Challenges with Existing Methods
The PC algorithm, while widespread, faces limitations due to the computational burden associated with learning the complete essential graph. This method relies on comprehensive conditional independence tests, which can be both time-consuming and subject to strong assumptions that are not always verifiable in practice.
Introducing Local Essential Graphs
To address these challenges, this study proposes an adaptation of the PC algorithm to focus on a more targeted approach: the Local Essential Graph (LEG). The LEG is defined relative to a specific target variable, thereby allowing for a more efficient extraction of the information necessary for identifying controlled direct effects. This localized approach minimizes the computational load while preserving the integrity of causal inference.
LocPC and LocPC-CDE Algorithms
The newly developed algorithms, LocPC and LocPC-CDE, are designed to streamline the identification of controlled direct effects. The LocPC algorithm leverages only local conditional independence tests, significantly reducing the number of tests required compared to global methods. Meanwhile, LocPC-CDE extracts precisely the necessary and sufficient portions of the LEG for CDE identification.
Advantages Over Traditional Methods
The key advantages of the proposed methods include:
- Reduced number of conditional independence tests required.
- Operational under weaker assumptions, enhancing applicability in various contexts.
- Theoretical guarantees that maintain the reliability of the results.
Conclusion
This innovative approach presents a significant advancement in the field of causal discovery. By focusing on local structures and minimizing computational demands, LocPC and LocPC-CDE provide a practical solution for researchers aiming to identify controlled direct effects in complex systems. The effectiveness of these algorithms has been validated through comprehensive testing on both synthetic and real datasets.
Future Directions
Further research will explore the applicability of these algorithms across various domains and their potential integration into existing causal inference frameworks.