mlsanityData to 7 Oct 2026

Finding Regions of Counterfactual Explanations via Robust Optimization

arXiv 2301.11113 ↗First posted 26 Jan 2023cs.LGcited by 19

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Abstract (arXiv)

Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this work we derive an iterative method to calculate robust CEs, i.e. CEs that remain valid even after the features are slightly perturbed. To this end, our method provides a whole region of CEs allowing the user to choose a suitable recourse to obtain a desired outcome. We use algorithmic ideas from robust optimization and prove convergence results for the most common machine learning methods including logistic regression, decision trees, random forests, and neural networks. Our experiments show that our method can efficiently generate globally optimal robust CEs for a variety of common data sets and classification models.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 22 of its 40 references that are in the map. First posted on arXiv 26 Jan 2023.

Builds on

22 of 40 references.

References · 22

  1. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,086
  2. 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 612
  3. 2018Actionable Recourse in Linear Classificationcited by 327
  4. 2019Model-Agnostic Counterfactual Explanations for Consequential Decisionscited by 204
  5. 2020Multi-Objective Counterfactual Explanationscited by 157
  6. 2019Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifierscited by 143
  7. 2018Strong mixed-integer programming formulations for trained neural networkscited by 115
  8. 2021Counterfactual Explanations Can Be Manipulatedcited by 113
  9. 2019Efficient Search for Diverse Coherent Explanationscited by 111
  10. 2021Towards Robust and Reliable Algorithmic Recoursecited by 101
  11. 2021On the Adversarial Robustness of Causal Algorithmic Recoursecited by 56
  12. 2022Robust Counterfactual Explanations for Tree-Based Ensemblescited by 49
10 more
  1. 2021Evaluating Robustness of Counterfactual Explanationscited by 41
  2. 2022Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recoursecited by 40
  3. 2021Consistent Counterfactuals for Deep Modelscited by 37
  4. 2021Optimal Counterfactual Explanations in Tree Ensemblescited by 36
  5. 2020Algorithmic Recourse in the Wild: Understanding the Impact of Data and Model Shiftscited by 34
  6. 2019ReLU Networks as Surrogate Models in Mixed-Integer Linear Programscited by 33
  7. 2022On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbationscited by 32
  8. 2021Mixed-Integer Optimization with Constraint Learningcited by 30
  9. 2022Counterfactual Plans under Distributional Ambiguitycited by 19
  10. 2022Counterfactual Explanations Using Optimization With Constraint Learningcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 7; 2025: 3; 2026: 3.

19 papers.

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  1. 2023Robust Counterfactual Explanations for Neural Networks With Probabilistic Guaranteescited by 45
  2. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  3. 2024Robust Counterfactual Explanations in Machine Learning: A Surveycited by 29
  4. 2023Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisationcited by 20
  5. 2023Generating robust counterfactual explanationscited by 13
  6. 2024Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Changecited by 10
  7. 2023Beyond Known Reality: Exploiting Counterfactual Explanations for Medical Researchcited by 9
  8. 2024Interval Abstractions for Robust Counterfactual Explanationscited by 7
  9. 2024Generating Likely Counterfactuals Using Sum-Product Networkscited by 6
  10. 2024Trust Regions for Explanations via Black-Box Probabilistic Certificationcited by 4
  11. 2025Counterfactual Explanations for Model Ensembles Using Entropic Risk Measurescited by 4
  12. 2024Guiding the generation of counterfactual explanations through temporal background knowledge for Predictive Process Monitoringcited by 3
7 more
  1. 2024Clinicians' Voice: Fundamental Considerations for XAI in Healthcarecited by 3
  2. 2025Generating Counterfactual Explanations Under Temporal Constraintscited by 3
  3. 2023Iterative Partial Fulfillment of Counterfactual Explanations: Benefits and Riskscited by 1
  4. 2025Understanding Fixed Predictions via Confined Regionscited by 1
  5. 2026Linear Model Extraction via Factual and Counterfactual Queriescited by 1
  6. 2026Structure-Aware Robust Counterfactual Explanations via Conditional Gaussian Network Classifierscited by 0
  7. 2026Improving understanding and trust in AI: How users benefit from interval-based counterfactual explanationscited by 0