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.

翻译：理解并充分评估真实因果图与学习因果图之间的差异对于干预下的因果推断至关重要。作为基于图的结构汉明距离和结构干预距离的扩展，我们提出了一种新的连续度量指标，该指标在计算真实因果图与学习因果图之间的差异时，除了考虑图结构外，还结合了底层数据。该距离基于将每对节点上的干预分布作为条件均值嵌入映射到再生核希尔伯特空间中，并通过最大（条件）均值差异来估计它们的差异。我们展示了理论结果，并通过合成数据的数值实验进行了验证。