Structural Intervention Distance (SID) for Evaluating Causal Graphs

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the so-called Structural Intervention Distance (SID). The SID is based on a graphical criterion only but nevertheless, it quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. In particular, SID is entirely different and much more appropriate for causal inference than the popular Structural Hamming Distance (SHD) between DAGs. We discuss properties of this distance and provide an efficient implementation.