A continuous Structural Intervention Distance to compare Causal Graphs

TL;DR

This paper introduces a new continuous metric for comparing causal graphs that incorporates data distribution differences, improving assessment of learned causal structures.

Contribution

It extends existing structural distances by embedding intervention distributions into reproducing kernel Hilbert spaces, providing a data-aware comparison method.

Findings

The proposed metric effectively captures differences between true and learned causal graphs.

Theoretical validation confirms the metric's consistency and robustness.

Numerical experiments demonstrate improved comparison accuracy over existing methods.

Abstract

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.