A continuous Structural Intervention Distance to compare Causal Graphs
This work addresses the need for more accurate causal graph comparison in causal inference, though it appears incremental as an extension of existing distances.
The authors tackled the problem of comparing true and learned causal graphs by proposing a continuous metric that incorporates both graph structure and underlying data, showing theoretical results validated with synthetic experiments.
Understanding and adequately assessing the difference between a true and a learnt causal graphs is crucial for causal inference under interventions. As an extension to the graph-based structural Hamming distance and structural intervention distance, we propose a novel continuous-measured metric that considers the underlying data in addition to the graph structure for its calculation of the difference between a true and a learnt causal graph. The distance is based on embedding intervention distributions over each pair of nodes as conditional mean embeddings into reproducing kernel Hilbert spaces and estimating their difference by the maximum (conditional) mean discrepancy. We show theoretical results which we validate with numerical experiments on synthetic data.