# A Few Good Counterfactuals: Generating Interpretable, Plausible and Diverse Counterfactual Explanations

arXiv: https://arxiv.org/abs/2101.09056 · HTML: https://mlsanity.com/paper/2101.09056/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 22 Jan 2021.

## Builds on (most cited first, 15 of 15)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Explaining Explanations in AI](https://mlsanity.com/paper/1811.01439/) (2018)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)
- [Instance-based Counterfactual Explanations for Time Series Classification](https://mlsanity.com/paper/2009.13211/) (2020)
- [Interpretable Credit Application Predictions With Counterfactual Explanations](https://mlsanity.com/paper/1811.05245/) (2018)
- [Counterfactual Explanation Algorithms for Behavioral and Textual Data](https://mlsanity.com/paper/1912.01819/) (2019)

## Built on by (most cited first, 19 of 19)

- [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)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [Counterfactual Explanations for Misclassified Images: How Human and Machine Explanations Differ](https://mlsanity.com/paper/2212.08733/) (2022)
- [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)
- ["Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations](https://mlsanity.com/paper/2211.14858/) (2022)
- [Generating collective counterfactual explanations in score-based classification via mathematical optimization](https://mlsanity.com/paper/2310.12822/) (2023)
- [Solving the Class Imbalance Problem Using a Counterfactual Method for Data Augmentation](https://mlsanity.com/paper/2111.03516/) (2021)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)
- [Even-Ifs From If-Onlys: Are the Best Semi-Factual Explanations Found Using Counterfactuals As Guides?](https://mlsanity.com/paper/2403.00980/) (2024)
- [T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems](https://mlsanity.com/paper/2309.16146/) (2023)
- [Explainable bank failure prediction models: Counterfactual explanations to reduce the failure risk](https://mlsanity.com/paper/2407.11089/) (2024)
- [Augmenting The Weather: A Hybrid Counterfactual-SMOTE Algorithm for Improving Crop Growth Prediction When Climate Changes](https://mlsanity.com/paper/2511.11945/) (2025)
- [Axiomatic Foundations of Counterfactual Explanations](https://mlsanity.com/paper/2602.04028/) (2026)
- [On the Connection between Game-Theoretic Feature Attributions and Counterfactual Explanations](https://mlsanity.com/paper/2307.06941/) (2023)
- [iSee: Advancing Multi-Shot Explainable AI Using Case-based Recommendations](https://mlsanity.com/paper/2408.12941/) (2024)
- [On the Hardness of Computing Counterfactual and Semifactual Explanations in XAI](https://mlsanity.com/paper/2601.09455/) (2026)
- [Explanations-Driven Active Feature Acquisition for Algorithmic Recourse](https://mlsanity.com/paper/2609.12179/) (2026)

## Abstract (arXiv)

Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate synthetic counterfactuals using blind perturbation. However, such methods have several shortcomings: the resulting counterfactuals (i) may not be valid data-points (they often use features that do not naturally occur), (ii) may lack the sparsity of good counterfactuals (if they modify too many features), and (iii) may lack diversity (if the generated counterfactuals are minimal variants of one another). We describe a method designed to overcome these problems, one that adapts native counterfactuals in the original dataset, to generate sparse, diverse synthetic counterfactuals from naturally occurring features. A series of experiments are reported that systematically explore parametric variations of this novel method on common datasets to establish the conditions for optimal performance.