Separation-based distance measures for causal graphs

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.