# Achieving Diversity in Counterfactual Explanations: a Review and Discussion arXiv: https://arxiv.org/abs/2305.05840 ยท HTML: https://mlsanity.com/paper/2305.05840/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Builds on 56 of its 86 references that are in the map. - First posted on arXiv 10 May 2023. ## Builds on (most cited first, 30 of 56) - [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017) - ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016) - [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017) - [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) - [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019) - [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018) - [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020) - [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019) - [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020) - [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019) - [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019) - [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020) - [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019) - [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019) - [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021) - [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021) - [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019) - [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019) - [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020) - [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021) - [Beyond Trivial Counterfactual Explanations with Diverse Valuable Explanations](https://mlsanity.com/paper/2103.10226/) (2021) - [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020) - [DECE: Decision Explorer with Counterfactual Explanations for Machine Learning Models](https://mlsanity.com/paper/2008.08353/) (2020) - [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021) - [Human Perceptions of Fairness in Algorithmic Decision Making: A Case Study of Criminal Risk Prediction](https://mlsanity.com/paper/1802.09548/) (2018) - [On the computation of counterfactual explanations -- A survey](https://mlsanity.com/paper/1911.07749/) (2019) - [Convex Density Constraints for Computing Plausible Counterfactual Explanations](https://mlsanity.com/paper/2002.04862/) (2020) ## Built on by (most cited first, 11 of 11) - [Fast Diffusion-Based Counterfactuals for Shortcut Removal and Generation](https://mlsanity.com/paper/2312.14223/) (2023) - [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024) - [Navigating Explanatory Multiverse Through Counterfactual Path Geometry](https://mlsanity.com/paper/2306.02786/) (2023) - [Prediction without Preclusion: Recourse Verification with Reachable Sets](https://mlsanity.com/paper/2308.12820/) (2023) - [DiCoFlex: Model-agnostic diverse counterfactuals with flexible control](https://mlsanity.com/paper/2505.23700/) (2025) - [Synthesising Counterfactual Explanations via Label-Conditional Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/2510.04855/) (2025) - [Learning local discrete features in explainable-by-design convolutional neural networks](https://mlsanity.com/paper/2411.00139/) (2024) - [Am I Being Treated Fairly? A Conceptual Framework for Individuals to Ascertain Fairness](https://mlsanity.com/paper/2504.02461/) (2025) - [DiCE-Extended: A Robust Approach to Counterfactual Explanations in Machine Learning](https://mlsanity.com/paper/2504.19027/) (2025) - [Onto-Epistemological Analysis of AI Explanations](https://mlsanity.com/paper/2510.02996/) (2025) - [ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material](https://mlsanity.com/paper/2605.30225/) (2026) ## Abstract (arXiv) In the field of Explainable Artificial Intelligence (XAI), counterfactual examples explain to a user the predictions of a trained decision model by indicating the modifications to be made to the instance so as to change its associated prediction. These counterfactual examples are generally defined as solutions to an optimization problem whose cost function combines several criteria that quantify desiderata for a good explanation meeting user needs. A large variety of such appropriate properties can be considered, as the user needs are generally unknown and differ from one user to another; their selection and formalization is difficult. To circumvent this issue, several approaches propose to generate, rather than a single one, a set of diverse counterfactual examples to explain a prediction. This paper proposes a review of the numerous, sometimes conflicting, definitions that have been proposed for this notion of diversity. It discusses their underlying principles as well as the hypotheses on the user needs they rely on and proposes to categorize them along several dimensions (explicit vs implicit, universe in which they are defined, level at which they apply), leading to the identification of further research challenges on this topic.