Simple k-RF Metrics for Comparison of Labeled DAGs

Causal relationships between different entities are often modeled as labeled acyclic digraphs (DAGs) in biology and healthcare, in particular for depicting the progression of malignant tumor cells. Comparison of labeled DAGs is essential for developing methods for inference and evaluation of DAG models. Therefore, a robust dissimilarity metric is critical for such comparison tasks. We introduce new dissimilarity measures for labeled DAGs by refining the k-Robinson-Foulds distance, originally defined to compare labeled trees. The new measures are defined based on the comparison of local node-induced multisets of labels. They can be used to compare DAGs with different label sets, without the need to introduce auxiliary nodes or remove existing ones.