Optimal Counterfactual Explanations in Tree Ensembles
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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
- 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,089
- 2018A Survey Of Methods For Explaining Black Box Modelscited by 973
- 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 614
- 2018Actionable Recourse in Linear Classificationcited by 328
- 2020Algorithmic Recourse: from Counterfactual Explanations to Interventionscited by 250
- 2019Model-Agnostic Counterfactual Explanations for Consequential Decisionscited by 204
- 2019Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifierscited by 144
- 2020A survey of algorithmic recourse: definitions, formulations, solutions, and prospectscited by 118
- 2019The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasonscited by 115
- 2019Efficient Search for Diverse Coherent Explanationscited by 111
- 2017Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweakingcited by 76
- 2019FOCUS: Flexible Optimizable Counterfactual Explanations for Tree Ensemblescited by 43
4 more
- 2020Born-Again Tree Ensemblescited by 38
- 2020Convex Density Constraints for Computing Plausible Counterfactual Explanationscited by 32
- 2020BRPO: Batch Residual Policy Optimizationcited by 25
- 2020Ordered Counterfactual Explanation by Mixed-Integer Linear Optimizationcited by 11
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Citing papers per year: 2022: 9; 2023: 12; 2024: 6; 2025: 3; 2026: 6.
36 papers.
Sort:
- 2023GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanationscited by 27
- 2022Computing Abductive Explanations for Boosted Treescited by 23
- 2023Finding Regions of Counterfactual Explanations via Robust Optimizationcited by 19
- 2023Efficient XAI Techniques: A Taxonomic Surveycited by 14
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
- 2024Trained Random Forests Completely Reveal your Datasetcited by 11
- 2022Global Counterfactual Explanations: Investigations, Implementations and Improvementscited by 9
- 2023Generating collective counterfactual explanations in score-based classification via mathematical optimizationcited by 9
- 2023The Risks of Recourse in Binary Classificationcited by 8
- 2022On the Safety of Interpretable Machine Learning: A Maximum Deviation Approachcited by 7
- 2023Explainable Data-Driven Optimization: From Context to Decision and Back Againcited by 7
- 2024Learning Decision Trees and Forests with Algorithmic Recoursecited by 7
24 more
- 2024Generating Likely Counterfactuals Using Sum-Product Networkscited by 6
- 2025Counterfactual Explanations for Model Ensembles Using Entropic Risk Measurescited by 5
- 2023Very fast, approximate counterfactual explanations for decision forestscited by 4
- 2023Prediction without Preclusion: Recourse Verification with Reachable Setscited by 4
- 2024Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensemblescited by 4
- 2025From Counterfactuals to Trees: Competitive Analysis of Model Extraction Attackscited by 3
- 2022Realistic Counterfactual Explanations with Learned Relationscited by 2
- 2022Don't Explain Noise: Robust Counterfactuals for Randomized Ensemblescited by 2
- 2022Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cutscited by 2
- 2023Algorithmic Recourse with Missing Valuescited by 2
- 2024One-for-many Counterfactual Explanations by Column Generationcited by 2
- 2026Counterfactual Maps: What They Are and How to Find Themcited by 2
- 2022Supervised Feature Compression based on Counterfactual Analysiscited by 1
- 2026PACE: Prune-And-Compress Ensemble Modelscited by 1
- 2026Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigmscited by 1
- 2022Local and Regional Counterfactual Rules: Summarized and Robust Recoursescited by 0
- 2022Decomposing Counterfactual Explanations for Consequential Decision Makingcited by 0
- 2023Inverse classification with logistic and softmax classifiers: efficient optimizationcited by 0
- 2023Explainable History Distillation by Marked Temporal Point Processcited by 0
- 2024Mining Action Rules for Defect Reduction Planningcited by 0
- 2025Actionable and diverse counterfactual explanations incorporating domain knowledge and plausibility constraintscited by 0
- 2026PINE: Pruning Boosted Tree Ensembles with Conformal In-Distribution Prediction Equivalencecited by 0
- 2026Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicitycited by 0
- 2026Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensemblescited by 0
- 2026Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles19 Aug 2026
- 2026Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity29 May 2026
- 2026PINE: Pruning Boosted Tree Ensembles with Conformal In-Distribution Prediction Equivalence27 May 2026
- 2026Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigms7 May 2026
- 2026PACE: Prune-And-Compress Ensemble Models7 May 2026
- 2026Counterfactual Maps: What They Are and How to Find Them9 Feb 2026
- 2025Actionable and diverse counterfactual explanations incorporating domain knowledge and plausibility constraints25 Nov 2025
- 2025Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures11 Mar 2025
- 2025From Counterfactuals to Trees: Competitive Analysis of Model Extraction Attacks7 Feb 2025
- 2024Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensembles28 Aug 2024
- 2024Learning Decision Trees and Forests with Algorithmic Recourse3 Jun 2024
- 2024Mining Action Rules for Defect Reduction Planning22 May 2024
24 more
- 2024Trained Random Forests Completely Reveal your Dataset29 Feb 2024
- 2024One-for-many Counterfactual Explanations by Column Generation12 Feb 2024
- 2024Generating Likely Counterfactuals Using Sum-Product Networks25 Jan 2024
- 2023Explainable History Distillation by Marked Temporal Point Process13 Nov 2023
- 2023Generating collective counterfactual explanations in score-based classification via mathematical optimization19 Oct 2023
- 2023Inverse classification with logistic and softmax classifiers: efficient optimization16 Sep 2023
- 2023Prediction without Preclusion: Recourse Verification with Reachable Sets24 Aug 2023
- 2023The Risks of Recourse in Binary Classification1 Jun 2023
- 2023GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations26 May 2023
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussion10 May 2023
- 2023Algorithmic Recourse with Missing Values28 Apr 2023
- 2023Very fast, approximate counterfactual explanations for decision forests6 Mar 2023
- 2023Efficient XAI Techniques: A Taxonomic Survey7 Feb 2023
- 2023Finding Regions of Counterfactual Explanations via Robust Optimization26 Jan 2023
- 2023Explainable Data-Driven Optimization: From Context to Decision and Back Again24 Jan 2023
- 2022Supervised Feature Compression based on Counterfactual Analysis17 Nov 2022
- 2022Decomposing Counterfactual Explanations for Consequential Decision Making3 Nov 2022
- 2022On the Safety of Interpretable Machine Learning: A Maximum Deviation Approach2 Nov 2022
- 2022Local and Regional Counterfactual Rules: Summarized and Robust Recourses29 Sep 2022
- 2022Computing Abductive Explanations for Boosted Trees16 Sep 2022
- 2022Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cuts15 Jul 2022
- 2022Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles27 May 2022
- 2022Global Counterfactual Explanations: Investigations, Implementations and Improvements14 Apr 2022
- 2022Realistic Counterfactual Explanations with Learned Relations15 Feb 2022
- 2023GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanationscited by 27
- 2022Computing Abductive Explanations for Boosted Treescited by 23
- 2023Finding Regions of Counterfactual Explanations via Robust Optimizationcited by 19
- 2023Efficient XAI Techniques: A Taxonomic Surveycited by 14
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
- 2024Trained Random Forests Completely Reveal your Datasetcited by 11
- 2022Global Counterfactual Explanations: Investigations, Implementations and Improvementscited by 9
- 2023Generating collective counterfactual explanations in score-based classification via mathematical optimizationcited by 9
- 2023The Risks of Recourse in Binary Classificationcited by 8
- 2022On the Safety of Interpretable Machine Learning: A Maximum Deviation Approachcited by 7
- 2023Explainable Data-Driven Optimization: From Context to Decision and Back Againcited by 7
- 2024Learning Decision Trees and Forests with Algorithmic Recoursecited by 7
12 most cited of 36 All 36 (JSON)
- 2026Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles19 Aug 2026
- 2026Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity29 May 2026
- 2026PINE: Pruning Boosted Tree Ensembles with Conformal In-Distribution Prediction Equivalence27 May 2026
- 2026Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigms7 May 2026
- 2026PACE: Prune-And-Compress Ensemble Models7 May 2026
- 2026Counterfactual Maps: What They Are and How to Find Them9 Feb 2026
- 2025Actionable and diverse counterfactual explanations incorporating domain knowledge and plausibility constraints25 Nov 2025
- 2025Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures11 Mar 2025
- 2025From Counterfactuals to Trees: Competitive Analysis of Model Extraction Attacks7 Feb 2025
- 2024Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensembles28 Aug 2024
- 2024Learning Decision Trees and Forests with Algorithmic Recourse3 Jun 2024
- 2024Mining Action Rules for Defect Reduction Planning22 May 2024
12 newest of 36 All 36 (JSON)