# Structural Intervention Distance (SID) for Evaluating Causal Graphs

arXiv: https://arxiv.org/abs/1306.1043 · HTML: https://mlsanity.com/paper/1306.1043/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2013.

## Built on by (most cited first, 14 of 14)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Emerging Synergies in Causality and Deep Generative Models: A Survey](https://mlsanity.com/paper/2301.12351/) (2023)
- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [On the Interventional Kullback-Leibler Divergence](https://mlsanity.com/paper/2302.05380/) (2023)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions](https://mlsanity.com/paper/2510.22298/) (2025)
- [Causal Learning in Biomedical Applications: Krebs Cycle as a Benchmark](https://mlsanity.com/paper/2406.15189/) (2024)
- [Scalable Time-Series Causal Discovery with Approximate Causal Ordering](https://mlsanity.com/paper/2409.05500/) (2024)
- [DAG Learning from Zero-Inflated Count Data Using Continuous Optimization](https://mlsanity.com/paper/2512.16233/) (2025)
- [Synthetic but Not Realistic: The Evaluation Challenge in Generative Modelling for Structured Electronic Medical Records](https://mlsanity.com/paper/2606.08903/) (2026)

## Abstract (arXiv)

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction).