发现因果顺序中可及节点数单调递增，可用于高效恢复因果关系。
A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs
- 基于可达节点数排序来推断因果顺序
- 可达节点数严格递增时唯一确定马尔可夫等价类
- 适用于评估因果发现算法的合成数据生成
基于埃爾多斯-雷尼和尺度不变随机图构造的随机有向无环图（DAG）广泛用于评估因果发现算法。我们发现，在此类DAG中，通过开放路径可达的节点集合（称为亲属）沿因果顺序单调增加。通过数值实验验证该模式的普遍性，并证明可利用亲属数量估计进行因果顺序恢复。文献中的许多模拟设置下，该方法能良好逼近真实因果顺序；我们进一步证明，亲属数严格递增时导致唯一的马尔可夫等价类。本文建议采样时间序列DAG作为替代方案，并讨论其对因果发现算法及其合成数据评估的影响。
原文摘要 · Abstract (English)
Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.
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