提出局部算法，高效识别受控直接效应。
Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects
- 基于目标变量构建局部本质图，仅用局部独立性检验
- 只需少量检验即可确定识别受控直接效应所需结构
- 适合高维数据中因果效应定位，比全局方法更鲁棒
识别受控直接效应（CDEs）在众多科学领域至关重要。尽管现有方法可在已知因果有向无环图（DAG）下实现这一目标，但实际中真实DAG通常未知。本质图表示由相同条件独立关系定义的DAG等价类，是更现实的替代方案，而PC算法是通过条件独立性检验学习本质图最常用的方法。然而，学习完整本质图计算成本高，且依赖难以验证的强假设。本文将PC算法改进为仅恢复识别CDE所必需的图结构部分。具体地，我们引入相对于目标变量定义的局部本质图（LEG），并提出LocPC算法，仅使用局部条件独立性检验学习LEG。在此基础上，我们构建LocPC-CDE，精确提取识别特定CDE所必需且充分的图部分。相比全局方法，本方法所需条件独立性检验更少，假设更弱，同时保持理论保证。我们在合成与真实数据上验证了方法的有效性。
原文摘要 · Abstract (English)
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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