Learning directed acyclic graphs (DAGs) to identify causal relations underlying observational data is crucial but also poses significant challenges. Recently, topology-based methods have emerged as a two-step approach to discovering DAGs by first learning the topological ordering of variables and then eliminating redundant edges, while ensuring that the graph remains acyclic. However, one limitation is that these methods would generate numerous spurious edges that require subsequent pruning. To overcome this limitation, in this paper, we propose an improvement to topology-based methods by introducing limited time series data, consisting of only two cross-sectional records that need not be adjacent in time and are subject to flexible timing. By incorporating conditional instrumental variables as exogenous interventions, we aim to identify descendant nodes for each variable. Following this line, we propose a hierarchical topological ordering algorithm with conditional independence test (HT-CIT), which enables the efficient learning of sparse DAGs with a smaller search space compared to other popular approaches. The HT-CIT algorithm greatly reduces the number of edges that need to be pruned. Empirical results from synthetic and real-world datasets demonstrate the superiority of the proposed HT-CIT algorithm.

通过引入有限时间序列数据和条件独立性检验，我们提出了一种层次拓扑排序算法（HT-CIT），以更高效地学习稀疏的有向无环图，从而比其他流行方法具有更小的搜索空间，并大大减少需要修剪的边的数量。来自合成和真实数据集的实证结果证明了所提出的HT-CIT算法的优越性。

带有条件独立性检验的层次化拓扑排序对有限时间序列的应用