mlsanityData to 14 Oct 2026

Optimal Counterfactual Explanations in Tree Ensembles

arXiv 2106.06631 ↗First posted 11 Jun 2021cs.LG math.OCcited by 36

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Abstract (arXiv)

Counterfactual explanations are usually generated through heuristics that are sensitive to the search's initial conditions. The absence of guarantees of performance and robustness hinders trustworthiness. In this paper, we take a disciplined approach towards counterfactual explanations for tree ensembles. We advocate for a model-based search aiming at "optimal" explanations and propose efficient mixed-integer programming approaches. We show that isolation forests can be modeled within our framework to focus the search on plausible explanations with a low outlier score. We provide comprehensive coverage of additional constraints that model important objectives, heterogeneous data types, structural constraints on the feature space, along with resource and actionability restrictions. Our experimental analyses demonstrate that the proposed search approach requires a computational effort that is orders of magnitude smaller than previous mathematical programming algorithms. It scales up to large data sets and tree ensembles, where it provides, within seconds, systematic explanations grounded on well-defined models solved to optimality.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Builds on 16 of its 33 references that are in the map. First posted on arXiv 11 Jun 2021.

Builds on

16 of 33 references.

References · 16

  1. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,089
  2. 2018A Survey Of Methods For Explaining Black Box Modelscited by 973
  3. 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 614
  4. 2018Actionable Recourse in Linear Classificationcited by 328
  5. 2020Algorithmic Recourse: from Counterfactual Explanations to Interventionscited by 250
  6. 2019Model-Agnostic Counterfactual Explanations for Consequential Decisionscited by 204
  7. 2019Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifierscited by 144
  8. 2020A survey of algorithmic recourse: definitions, formulations, solutions, and prospectscited by 118
  9. 2019The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasonscited by 115
  10. 2019Efficient Search for Diverse Coherent Explanationscited by 111
  11. 2017Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweakingcited by 76
  12. 2019FOCUS: Flexible Optimizable Counterfactual Explanations for Tree Ensemblescited by 43
4 more
  1. 2020Born-Again Tree Ensemblescited by 38
  2. 2020Convex Density Constraints for Computing Plausible Counterfactual Explanationscited by 32
  3. 2020BRPO: Batch Residual Policy Optimizationcited by 25
  4. 2020Ordered Counterfactual Explanation by Mixed-Integer Linear Optimizationcited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 9; 2023: 12; 2024: 6; 2025: 3; 2026: 6.

36 papers.

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  1. 2023GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanationscited by 27
  2. 2022Computing Abductive Explanations for Boosted Treescited by 23
  3. 2023Finding Regions of Counterfactual Explanations via Robust Optimizationcited by 19
  4. 2023Efficient XAI Techniques: A Taxonomic Surveycited by 14
  5. 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
  6. 2024Trained Random Forests Completely Reveal your Datasetcited by 11
  7. 2022Global Counterfactual Explanations: Investigations, Implementations and Improvementscited by 9
  8. 2023Generating collective counterfactual explanations in score-based classification via mathematical optimizationcited by 9
  9. 2023The Risks of Recourse in Binary Classificationcited by 8
  10. 2022On the Safety of Interpretable Machine Learning: A Maximum Deviation Approachcited by 7
  11. 2023Explainable Data-Driven Optimization: From Context to Decision and Back Againcited by 7
  12. 2024Learning Decision Trees and Forests with Algorithmic Recoursecited by 7
24 more
  1. 2024Generating Likely Counterfactuals Using Sum-Product Networkscited by 6
  2. 2025Counterfactual Explanations for Model Ensembles Using Entropic Risk Measurescited by 5
  3. 2023Very fast, approximate counterfactual explanations for decision forestscited by 4
  4. 2023Prediction without Preclusion: Recourse Verification with Reachable Setscited by 4
  5. 2024Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensemblescited by 4
  6. 2025From Counterfactuals to Trees: Competitive Analysis of Model Extraction Attackscited by 3
  7. 2022Realistic Counterfactual Explanations with Learned Relationscited by 2
  8. 2022Don't Explain Noise: Robust Counterfactuals for Randomized Ensemblescited by 2
  9. 2022Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cutscited by 2
  10. 2023Algorithmic Recourse with Missing Valuescited by 2
  11. 2024One-for-many Counterfactual Explanations by Column Generationcited by 2
  12. 2026Counterfactual Maps: What They Are and How to Find Themcited by 2
  13. 2022Supervised Feature Compression based on Counterfactual Analysiscited by 1
  14. 2026PACE: Prune-And-Compress Ensemble Modelscited by 1
  15. 2026Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigmscited by 1
  16. 2022Local and Regional Counterfactual Rules: Summarized and Robust Recoursescited by 0
  17. 2022Decomposing Counterfactual Explanations for Consequential Decision Makingcited by 0
  18. 2023Inverse classification with logistic and softmax classifiers: efficient optimizationcited by 0
  19. 2023Explainable History Distillation by Marked Temporal Point Processcited by 0
  20. 2024Mining Action Rules for Defect Reduction Planningcited by 0
  21. 2025Actionable and diverse counterfactual explanations incorporating domain knowledge and plausibility constraintscited by 0
  22. 2026PINE: Pruning Boosted Tree Ensembles with Conformal In-Distribution Prediction Equivalencecited by 0
  23. 2026Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicitycited by 0
  24. 2026Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensemblescited by 0