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。