Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal graphs. However, many state-of-the-art causal discovery methods do not output single causal graphs, but rather their Markov equivalence classes (MECs) which encode all of the graph's separation and connection statements. In this work, we propose additional measures of distance that capture the difference in separations of two causal graphs which link-based distances are not fit to assess. The proposed distances have low polynomial time complexity and are applicable to directed acyclic graphs (DAGs) as well as to maximal ancestral graph (MAGs) that may contain bidirected edges. We complement our theoretical analysis with toy examples and empirical experiments that highlight the differences to existing comparison metrics.

翻译：评估因果发现算法输出的准确性对于开发和比较新方法至关重要。结构汉明距离等常用评估指标可用于评估因果图的各个链接。然而，许多最先进的因果发现方法并不输出单一的因果图，而是输出其马尔可夫等价类（MECs），这些等价类编码了图的所有分离与连接关系。在本研究中，我们提出了额外的距离度量方法，用于捕捉两个因果图在分离关系上的差异，这是基于链接的距离度量所无法评估的。所提出的距离度量具有较低的多项式时间复杂度，适用于有向无环图（DAGs）以及可能包含双向边的最大祖先图（MAGs）。我们通过理论分析、示例演示和实证实验，补充说明了所提方法与现有比较指标之间的差异。