Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects
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Abstract (arXiv)
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.
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References · 11
- 2013Direct and Indirect Effectscited by 280
- 2013Causal Inference and Causal Explanation with Background Knowledgecited by 170
- 2022Deep End-to-end Causal Inferencecited by 95
- 2013Learning Equivalence Classes of Bayesian Networks Structurescited by 77
- 2013Learning Sparse Causal Models is not NP-hardcited by 49
- 2023Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loopscited by 30
- 2023Case Studies of Causal Discovery from IT Monitoring Time Seriescited by 14
- 2024Local Causal Structure Learning in the Presence of Latent Variablescited by 11
- 2022Valid Inference After Causal Discoverycited by 10
- 2023Local Causal Discovery for Estimating Causal Effectscited by 10
- 2024Post-selection inference for causal effects after causal discoverycited by 7
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