# Convex Density Constraints for Computing Plausible Counterfactual Explanations

arXiv: https://arxiv.org/abs/2002.04862 · HTML: https://mlsanity.com/paper/2002.04862/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 30 of 32)

- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021)
- [Counterfactual Explanations for Arbitrary Regression Models](https://mlsanity.com/paper/2106.15212/) (2021)
- [A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Data](https://mlsanity.com/paper/2107.04680/) (2021)
- [Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Setting](https://mlsanity.com/paper/2205.05515/) (2022)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [Let's Go to the Alien Zoo: Introducing an Experimental Framework to Study Usability of Counterfactual Explanations for Machine Learning](https://mlsanity.com/paper/2205.03398/) (2022)
- ["Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations](https://mlsanity.com/paper/2211.14858/) (2022)
- [CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows](https://mlsanity.com/paper/2303.14668/) (2023)
- [Explaining Reject Options of Learning Vector Quantization Classifiers](https://mlsanity.com/paper/2202.07244/) (2022)
- [Model Agnostic Local Explanations of Reject](https://mlsanity.com/paper/2205.07623/) (2022)
- [Convex optimization for actionable & plausible counterfactual explanations](https://mlsanity.com/paper/2105.07630/) (2021)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [A Survey of Privacy-Preserving Model Explanations: Privacy Risks, Attacks, and Countermeasures](https://mlsanity.com/paper/2404.00673/) (2024)
- [CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forests](https://mlsanity.com/paper/2404.03506/) (2024)
- [Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels](https://mlsanity.com/paper/2405.17642/) (2024)
- [Generating Feasible and Plausible Counterfactual Explanations for Outcome Prediction of Business Processes](https://mlsanity.com/paper/2403.09232/) (2024)
- [Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles](https://mlsanity.com/paper/2205.14116/) (2022)
- [Contrastive Explanations for Explaining Model Adaptations](https://mlsanity.com/paper/2104.02459/) (2021)
- [Causality-based Counterfactual Explanation for Classification Models](https://mlsanity.com/paper/2105.00703/) (2021)
- [S-CFE: Simple Counterfactual Explanations](https://mlsanity.com/paper/2410.15723/) (2024)
- [Generative Example-Based Explanations: Bridging the Gap between Generative Modeling and Explainability](https://mlsanity.com/paper/2410.20890/) (2024)
- [Natural Counterfactuals With Necessary Backtracking](https://mlsanity.com/paper/2402.01607/) (2024)
- [HyConEx: Hypernetwork classifier with counterfactual explanations for tabular data](https://mlsanity.com/paper/2503.12525/) (2025)
- [Interpretable Event Diagnosis in Water Distribution Networks](https://mlsanity.com/paper/2505.07299/) (2025)
- [RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations](https://mlsanity.com/paper/2508.10455/) (2025)
- [On the Hardness of Computing Counterfactual and Semifactual Explanations in XAI](https://mlsanity.com/paper/2601.09455/) (2026)
- [A Probabilistic Consensus-Driven Approach for Robust Counterfactual Explanations](https://mlsanity.com/paper/2604.17494/) (2026)

## 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.