For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In the setting of linear structural equation models without bows, we study algebraic constraints and argue that these provide the most fine-grained resolution achievable. We propose efficient algorithms that decide whether two graphs impose the same algebraic constraints, or whether the constraints imposed by one graph are a subset of those imposed by another graph.

翻译：在存在潜在混杂因子的因果发现中，存在超越条件独立性的约束条件，这些约束能使因果发现算法区分更多图结构对。此类约束尚未得到充分理解。在线性结构方程模型的无弓形设定下，我们研究代数约束并论证其能提供可达到的最细粒度分辨力。我们提出高效算法，用于判定两个图是否施加相同的代数约束，或一个图施加的约束是否为另一图施加约束的子集。