mlsanityData to 7 Oct 2026

Adjustment Identification Distance: A gadjid for Causal Structure Learning

arXiv 2402.08616 ↗First posted 13 Feb 2024stat.ML cs.LG stat.MEcited by 16

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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.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 23 of its 54 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

23 of 54 references.

References · 23

  1. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  2. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  3. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 168
  4. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  5. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  6. 2017Causal Structure Learningcited by 84
  7. 2013Learning Equivalence Classes of Bayesian Networks Structurescited by 75
  8. 2020A Refined Laser Method and Faster Matrix Multiplicationcited by 56
  9. 2018On Causal Discovery with Equal Variance Assumptioncited by 55
  10. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  11. 2019The Case for Evaluating Causal Models Using Interventional Measures and Empirical Datacited by 30
  12. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
11 more
  1. 2022Evaluation Methods and Measures for Causal Learning Algorithmscited by 23
  2. 2014Estimating the effect of joint interventions from observational data in sparse high-dimensional settingscited by 20
  3. 2013Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)cited by 18
  4. 2020Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-valuescited by 18
  5. 2021Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithmscited by 11
  6. 2019Evaluating structure learning algorithms with a balanced scoring functioncited by 10
  7. 2024Separation-based distance measures for causal graphscited by 9
  8. 2020Evaluation of Causal Structure Learning Algorithms via Risk Estimationcited by 8
  9. 2020A Ladder of Causal Distancescited by 7
  10. 2022Linear-Time Algorithms for Front-Door Adjustment in Causal Graphscited by 4
  11. 2023A continuous Structural Intervention Distance to compare Causal Graphscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 9; 2026: 4.

16 papers.

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  1. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  2. 2024Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orderscited by 6
  3. 2024Are you doing better than random guessing? A call for using negative controls when evaluating causal discovery algorithmscited by 5
  4. 2026CauScale: Neural Causal Discovery at Scalecited by 5
  5. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  6. 2025SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graphcited by 3
  7. 2025Nonlinear Causal Discovery for Grouped Datacited by 3
  8. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  9. 2025Meta-Dependence in Conditional Independence Testingcited by 1
  10. 2025Generating Hypotheses of Dynamic Causal Graphs in Neuroscience: Leveraging Generative Factor Models of Observed Time Seriescited by 1
  11. 2025How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errorscited by 0
  12. 2025Linear-Time Primitives for Algorithm Development in Graphical Causal Inferencecited by 0
4 more
  1. 2025Practical Causal Evaluation Metrics for Biological Networkscited by 0
  2. 2026A Topological Sorting Criterion for Random Causal Directed Acyclic Graphscited by 0
  3. 2026TriOpt: A Scalable Algorithm for Linear Causal Discoverycited by 0
  4. 2026Verifying formulas for interventional distributionscited by 0