# Adjustment Identification Distance: A gadjid for Causal Structure Learning

arXiv: https://arxiv.org/abs/2402.08616 · HTML: https://mlsanity.com/paper/2402.08616/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [A Refined Laser Method and Faster Matrix Multiplication](https://mlsanity.com/paper/2010.05846/) (2020)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data](https://mlsanity.com/paper/1910.05387/) (2019)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Evaluation Methods and Measures for Causal Learning Algorithms](https://mlsanity.com/paper/2202.02896/) (2022)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values](https://mlsanity.com/paper/2002.09573/) (2020)
- [Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms](https://mlsanity.com/paper/2107.03863/) (2021)
- [Evaluating structure learning algorithms with a balanced scoring function](https://mlsanity.com/paper/1905.12666/) (2019)
- [Separation-based distance measures for causal graphs](https://mlsanity.com/paper/2402.04952/) (2024)
- [Evaluation of Causal Structure Learning Algorithms via Risk Estimation](https://mlsanity.com/paper/2006.15387/) (2020)
- [A Ladder of Causal Distances](https://mlsanity.com/paper/2005.02480/) (2020)
- [Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs](https://mlsanity.com/paper/2211.16468/) (2022)
- [A continuous Structural Intervention Distance to compare Causal Graphs](https://mlsanity.com/paper/2307.16452/) (2023)

## Built on by (most cited first, 16 of 16)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [CauScale: Neural Causal Discovery at Scale](https://mlsanity.com/paper/2602.08629/) (2026)
- [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)
- [Nonlinear Causal Discovery for Grouped Data](https://mlsanity.com/paper/2506.05120/) (2025)
- [Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning](https://mlsanity.com/paper/2510.04970/) (2025)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors](https://mlsanity.com/paper/2502.14719/) (2025)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [Meta-Dependence in Conditional Independence Testing](https://mlsanity.com/paper/2504.12594/) (2025)
- [Generating Hypotheses of Dynamic Causal Graphs in Neuroscience: Leveraging Generative Factor Models of Observed Time Series](https://mlsanity.com/paper/2505.20697/) (2025)
- [Linear-Time Primitives for Algorithm Development in Graphical Causal Inference](https://mlsanity.com/paper/2506.15758/) (2025)
- [Practical Causal Evaluation Metrics for Biological Networks](https://mlsanity.com/paper/2511.12805/) (2025)
- [A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs](https://mlsanity.com/paper/2605.06288/) (2026)
- [TriOpt: A Scalable Algorithm for Linear Causal Discovery](https://mlsanity.com/paper/2605.17465/) (2026)
- [Verifying formulas for interventional distributions](https://mlsanity.com/paper/2607.13883/) (2026)

## Abstract (arXiv)

Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We introduce a framework for developing causal distances between graphs which includes the structural intervention distance for directed acyclic graphs as a special case. We use this framework to develop improved adjustment-based distances as well as extensions to completed partially directed acyclic graphs and causal orders. We develop new reachability algorithms to compute the distances efficiently and to prove their low polynomial time complexity. In our package gadjid (open source at https://github.com/CausalDisco/gadjid), we provide implementations of our distances; they are orders of magnitude faster with proven lower time complexity than the structural intervention distance and thereby provide a success metric for causal discovery that scales to graph sizes that were previously prohibitive.