# Separation-based distance measures for causal graphs

arXiv: https://arxiv.org/abs/2402.04952 · HTML: https://mlsanity.com/paper/2402.04952/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2102.10324/) (2021)
- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Toward Falsifying Causal Graphs Using a Permutation-Based Test](https://mlsanity.com/paper/2305.09565/) (2023)
- [Robustness of Algorithms for Causal Structure Learning to Hyperparameter Choice](https://mlsanity.com/paper/2310.18212/) (2023)

## Built on by (most cited first, 9 of 9)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Are you doing better than random guessing? A call for using negative controls when evaluating causal discovery algorithms](https://mlsanity.com/paper/2412.10039/) (2024)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [Meta-Dependence in Conditional Independence Testing](https://mlsanity.com/paper/2504.12594/) (2025)
- [Measuring Similarity in Causal Graphs: A Framework for Semantic and Structural Analysis](https://mlsanity.com/paper/2503.11046/) (2025)
- [Graph Distance Based on Cause-Effect Estimands with Latents](https://mlsanity.com/paper/2510.25037/) (2025)
- [Causal Modeling of Adverse Pregnancy Outcomes via Adaptive LLM Proposals](https://mlsanity.com/paper/2608.21079/) (2026)

## Abstract (arXiv)

Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal graphs. However, many state-of-the-art causal discovery methods do not output single causal graphs, but rather their Markov equivalence classes (MECs) which encode all of the graph's separation and connection statements. In this work, we propose additional measures of distance that capture the difference in separations of two causal graphs which link-based distances are not fit to assess. The proposed distances have low polynomial time complexity and are applicable to directed acyclic graphs (DAGs) as well as to maximal ancestral graph (MAGs) that may contain bidirected edges. We complement our theoretical analysis with toy examples and empirical experiments that highlight the differences to existing comparison metrics.