Convex Density Constraints for Computing Plausible Counterfactual Explanations
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Abstract (arXiv)
The increasing deployment of machine learning as well as legal regulations such as EU's GDPR cause a need for user-friendly explanations of decisions proposed by machine learning models. Counterfactual explanations are considered as one of the most popular techniques to explain a specific decision of a model. While the computation of "arbitrary" counterfactual explanations is well studied, it is still an open research problem how to efficiently compute plausible and feasible counterfactual explanations. We build upon recent work and propose and study a formal definition of plausible counterfactual explanations. In particular, we investigate how to use density estimators for enforcing plausibility and feasibility of counterfactual explanations. For the purpose of efficient computations, we propose convex density constraints that ensure that the resulting counterfactual is located in a region of the data space of high density.
Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Feb 2020.
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Citing papers per year: 2021: 8; 2022: 6; 2023: 2; 2024: 9; 2025: 3; 2026: 4.
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- 2021If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniquescited by 82
- 2021Evaluating Robustness of Counterfactual Explanationscited by 41
- 2021Optimal Counterfactual Explanations in Tree Ensemblescited by 36
- 2021Counterfactual Explanations for Arbitrary Regression Modelscited by 22
- 2021A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Datacited by 19
- 2022Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Settingcited by 11
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
- 2024Probabilistically Plausible Counterfactual Explanations with Normalizing Flowscited by 11
- 2022Let's Go to the Alien Zoo: Introducing an Experimental Framework to Study Usability of Counterfactual Explanations for Machine Learningcited by 9
- 2022"Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanationscited by 9
- 2023CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flowscited by 8
- 2022Explaining Reject Options of Learning Vector Quantization Classifierscited by 7
20 more
- 2022Model Agnostic Local Explanations of Rejectcited by 7
- 2021Convex optimization for actionable & plausible counterfactual explanationscited by 6
- 2024Generating Likely Counterfactuals Using Sum-Product Networkscited by 6
- 2024A Survey of Privacy-Preserving Model Explanations: Privacy Risks, Attacks, and Countermeasurescited by 6
- 2024CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forestscited by 5
- 2024Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levelscited by 5
- 2024Generating Feasible and Plausible Counterfactual Explanations for Outcome Prediction of Business Processescited by 4
- 2022Don't Explain Noise: Robust Counterfactuals for Randomized Ensemblescited by 2
- 2021Contrastive Explanations for Explaining Model Adaptationscited by 1
- 2021Causality-based Counterfactual Explanation for Classification Modelscited by 1
- 2024S-CFE: Simple Counterfactual Explanationscited by 1
- 2024Generative Example-Based Explanations: Bridging the Gap between Generative Modeling and Explainabilitycited by 1
- 2024Natural Counterfactuals With Necessary Backtrackingcited by 0
- 2025HyConEx: Hypernetwork classifier with counterfactual explanations for tabular datacited by 0
- 2025Interpretable Event Diagnosis in Water Distribution Networkscited by 0
- 2025RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanationscited by 0
- 2026On the Hardness of Computing Counterfactual and Semifactual Explanations in XAIcited by 0
- 2026A Probabilistic Consensus-Driven Approach for Robust Counterfactual Explanationscited by 0
- 2026CEL: Comprehensive Counterfactual Explanations Library and Benchmarkcited by 0
- 2026Diversified and Perceptible Counterfactual Examples Leveraging Expert Knowledgecited by 0
- 2026Diversified and Perceptible Counterfactual Examples Leveraging Expert Knowledge14 Sep 2026
- 2026CEL: Comprehensive Counterfactual Explanations Library and Benchmark24 Jul 2026
- 2026A Probabilistic Consensus-Driven Approach for Robust Counterfactual Explanations19 Apr 2026
- 2026On the Hardness of Computing Counterfactual and Semifactual Explanations in XAI14 Jan 2026
- 2025RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations14 Aug 2025
- 2025Interpretable Event Diagnosis in Water Distribution Networks12 May 2025
- 2025HyConEx: Hypernetwork classifier with counterfactual explanations for tabular data16 Mar 2025
- 2024Generative Example-Based Explanations: Bridging the Gap between Generative Modeling and Explainability28 Oct 2024
- 2024S-CFE: Simple Counterfactual Explanations21 Oct 2024
- 2024Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels27 May 2024
- 2024Probabilistically Plausible Counterfactual Explanations with Normalizing Flows27 May 2024
- 2024CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forests4 Apr 2024
20 more
- 2024A Survey of Privacy-Preserving Model Explanations: Privacy Risks, Attacks, and Countermeasures31 Mar 2024
- 2024Generating Feasible and Plausible Counterfactual Explanations for Outcome Prediction of Business Processes14 Mar 2024
- 2024Natural Counterfactuals With Necessary Backtracking2 Feb 2024
- 2024Generating Likely Counterfactuals Using Sum-Product Networks25 Jan 2024
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussion10 May 2023
- 2023CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows26 Mar 2023
- 2022"Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations27 Nov 2022
- 2022Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles27 May 2022
- 2022Model Agnostic Local Explanations of Reject16 May 2022
- 2022Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Setting11 May 2022
- 2022Let's Go to the Alien Zoo: Introducing an Experimental Framework to Study Usability of Counterfactual Explanations for Machine Learning6 May 2022
- 2022Explaining Reject Options of Learning Vector Quantization Classifiers15 Feb 2022
- 2021A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Data9 Jul 2021
- 2021Counterfactual Explanations for Arbitrary Regression Models29 Jun 2021
- 2021Optimal Counterfactual Explanations in Tree Ensembles11 Jun 2021
- 2021Convex optimization for actionable & plausible counterfactual explanations17 May 2021
- 2021Causality-based Counterfactual Explanation for Classification Models3 May 2021
- 2021Contrastive Explanations for Explaining Model Adaptations6 Apr 2021
- 2021Evaluating Robustness of Counterfactual Explanations3 Mar 2021
- 2021If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques26 Feb 2021
- 2021If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniquescited by 82
- 2021Evaluating Robustness of Counterfactual Explanationscited by 41
- 2021Optimal Counterfactual Explanations in Tree Ensemblescited by 36
- 2021Counterfactual Explanations for Arbitrary Regression Modelscited by 22
- 2021A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Datacited by 19
- 2022Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Settingcited by 11
- 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
- 2024Probabilistically Plausible Counterfactual Explanations with Normalizing Flowscited by 11
- 2022Let's Go to the Alien Zoo: Introducing an Experimental Framework to Study Usability of Counterfactual Explanations for Machine Learningcited by 9
- 2022"Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanationscited by 9
- 2023CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flowscited by 8
- 2022Explaining Reject Options of Learning Vector Quantization Classifierscited by 7
12 most cited of 32 All 32 (JSON)
- 2026Diversified and Perceptible Counterfactual Examples Leveraging Expert Knowledge14 Sep 2026
- 2026CEL: Comprehensive Counterfactual Explanations Library and Benchmark24 Jul 2026
- 2026A Probabilistic Consensus-Driven Approach for Robust Counterfactual Explanations19 Apr 2026
- 2026On the Hardness of Computing Counterfactual and Semifactual Explanations in XAI14 Jan 2026
- 2025RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations14 Aug 2025
- 2025Interpretable Event Diagnosis in Water Distribution Networks12 May 2025
- 2025HyConEx: Hypernetwork classifier with counterfactual explanations for tabular data16 Mar 2025
- 2024Generative Example-Based Explanations: Bridging the Gap between Generative Modeling and Explainability28 Oct 2024
- 2024S-CFE: Simple Counterfactual Explanations21 Oct 2024
- 2024Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels27 May 2024
- 2024Probabilistically Plausible Counterfactual Explanations with Normalizing Flows27 May 2024
- 2024CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forests4 Apr 2024
12 newest of 32 All 32 (JSON)