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Causal inference relies on the structure of a graph, often a directed acyclicgraph (DAG). Different graphs may result in different causal inferencestatements and different intervention distributions. To quantify suchdifferences, we propose a (pre-) distance between DAGs, the structuralintervention distance (SID). The SID is based on a graphical criterion only andquantifies the closeness between two DAGs in terms of their correspondingcausal inference statements. It is therefore well-suited for evaluating graphsthat are used for computing interventions. Instead of DAGs it is also possibleto compare CPDAGs, completed partially directed acyclic graphs that representMarkov equivalence classes. Since it differs significantly from the popularStructural Hamming Distance (SHD), the SID constitutes a valuable additionalmeasure. We discuss properties of this distance and provide an efficientimplementation with software code available on the first author's homepage (anR package is under construction).

Structural Intervention Distance (SID) for Evaluating Causal Graphs