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.

学习因果结构及定向数据是一个根本性问题，具有广泛的应用领域。通过引入 Meek 分隔子，我们介绍了一种寻找具有小规模 Meek 分隔子的高效算法，用于部分搜索和因果匹配问题，从而实现对两个问题的对数逼近，并提供了首个已知的平均情况可证实保证。这为解决其他各种应用中出现的有目标因果结构学习问题的近乎最优方法的设计提供了可能性。

弱分隔符及其在有目标因果推断中的应用

Meek Separators and Their Applications in Targeted Causal Discovery

Existing approximate nearest neighbor search systems suffer from two
fundamental problems that are of practical importance but have not received
sufficient attention from the research community. First, although existing
systems perform well for the whole database, it is difficult to run a search
over a subset of the database. Second, there has been no discussion concerning
the performance decrement after many items have been newly added to a system.
We develop a reconfigurable inverted index (Rii) to resolve these two issues.
Based on the standard IVFADC system, we design a data layout such that items
are stored linearly. This enables us to efficiently run a subset search by
switching the search method to a linear PQ scan if the size of a subset is
small. Owing to the linear layout, the data structure can be dynamically
adjusted after new items are added, maintaining the fast speed of the system.
Extensive comparisons show that Rii achieves a comparable performance with
state-of-the art systems such as Faiss.

本文提出了一种可重构倒排索引（Rii）以解决近似最近邻搜索系统的两个重要问题：运行子集搜索困难和新项目增加后性能下降。基于标准 IVFADC 系统，Rii 设计了一种数据布局方法，使得项目被线性存储。由于线性布局，数据结构可以动态调整，维护系统的高速度。大量比较表明，Rii 与 Faiss 等最先进的系统相比具有可比较的性能。