Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called $targeted$ causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases. Towards this, we introduce the $Meek~separator$, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.

翻译：从干预数据中学习因果结构是一个基础性问题，广泛应用于各个领域。尽管许多先前工作聚焦于恢复完整因果图，但在实际场景中，有时仅需学习部分因果图即可满足需求，这被称为**目标因果发现**。本研究聚焦于两个具有充分动机的子问题：子集搜索与因果匹配。我们的目标是最小化两种情形下的干预次数。为此，我们引入**Meek隔离器**——一个顶点子集，对其施加干预后，可将剩余未定向边分解为更小的连通分量。我们进一步提出一种高效算法，用于寻找规模较小的Meek隔离器。该算法有助于设计各类分治策略。特别地，我们分别提出两种随机算法，对子集搜索和因果匹配实现了对数近似。我们的结果为这两个问题提供了首个平均情况下的理论保证。我们相信，这为设计针对各种应用中出现的其他目标因果结构学习问题的近最优方法开辟了可能性。