A continuous Structural Intervention Distance to compare Causal Graphs
Mihir Dhanakshirur Felix Laumann Junhyung Park Mauricio Barahona
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.