# A continuous Structural Intervention Distance to compare Causal Graphs

arXiv: https://arxiv.org/abs/2307.16452 · HTML: https://mlsanity.com/paper/2307.16452/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Learning and Testing Causal Models with Interventions](https://mlsanity.com/paper/1805.09697/) (2018)
- [A Ladder of Causal Distances](https://mlsanity.com/paper/2005.02480/) (2020)
- [Comparative Benchmarking of Causal Discovery Techniques](https://mlsanity.com/paper/1708.06246/) (2017)
- [Evaluating Causal Models by Comparing Interventional Distributions](https://mlsanity.com/paper/1608.04698/) (2016)

## Built on by (most cited first, 3 of 3)

- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Practical Causal Evaluation Metrics for Biological Networks](https://mlsanity.com/paper/2511.12805/) (2025)
- [Rethinking Generative Reconstruction Attacks against Graph Neural Network Models](https://mlsanity.com/paper/2606.29748/) (2026)

## Abstract (arXiv)

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.