发表机构
University of Amsterdam; University of Copenhagen（阿姆斯特丹大学; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对干预数据的簇DAG学习问题，提出首个基于评分的方法COARSE，其边阶段速度较最优方法提升两个数量级，在合成与真实数据上性能相当且运行高效。
AI 中文摘要
因果抽象的图方法将大量观测变量构成的低层因果有向无环图（DAG）转换为规模更小的高层DAG，其节点对原变量进行聚类，边则总结聚类间的因果关系。这类簇DAG更易解释，但学习它们需要找到聚类并恢复聚类间的边。Madaleno等人（2026）在两个基于约束的阶段中学习干预粗化（即合并干预无法区分变量的簇DAG）：先确定聚类，再确定边。我们提出COARSE，这是首个针对该任务的基于评分的方法：它保留两阶段结构，但在线性高斯假设下，将基于约束的边阶段替换为基于评分的阶段。我们证明干预本身可确定聚类间的因果顺序，且在聚类级BIC评分下，边的学习简化为每个聚类的单次局部搜索。我们证明该过程在多项式时间内运行，且只要每个干预影响的变量被正确识别，该方法是一致的。在合成与真实干预数据上，COARSE在样本量充足时达到与当前最优方法相当的边恢复性能，且边阶段速度最高提升两个数量级，包括在含数百个节点的稠密图上。
英文摘要
Graphical approaches to causal abstraction transform a low-level causal directed acyclic graph (DAG) over many measured variables into a smaller, high-level DAG whose nodes cluster the original variables and whose edges summarize the causal relations between clusters. Such cluster DAGs are easier to interpret, but learning them requires finding the clusters and recovering the edges between them. Madaleno et al. (2026) learn the interventional coarsening (the cluster DAG that merges variables the interventions cannot distinguish) in two constraint-based phases: first the clusters, then the edges. We introduce COARSE, the first score-based method for this task: it keeps the two-phase structure but, under linear Gaussian assumptions, swaps the constraint-based edge phase for a score-based one. We show that the interventions themselves identify a causal order over the clusters, and learning the edges reduces to a single local search per cluster under a cluster-level BIC score. We prove that the procedure runs in polynomial time and, provided the variables affected by each intervention are correctly identified, that it is consistent. On synthetic and real-world interventional data, COARSE matches state-of-the-art edge recovery given enough samples, with an edge phase up to two orders of magnitude faster, including on dense graphs with hundreds of nodes.
