# A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations

arXiv: https://arxiv.org/abs/2403.01221 · HTML: https://mlsanity.com/paper/2403.01221/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 13 of 13)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [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)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations](https://mlsanity.com/paper/2305.17021/) (2023)
- [Bias and Discrimination in AI: a cross-disciplinary perspective](https://mlsanity.com/paper/2008.07309/) (2020)
- [Promoting Counterfactual Robustness through Diversity](https://mlsanity.com/paper/2312.06564/) (2023)
- [Explaining Groups of Points in Low-Dimensional Representations](https://mlsanity.com/paper/2003.01640/) (2020)
- ["Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations](https://mlsanity.com/paper/2211.14858/) (2022)
- [Explaining Groups of Instances Counterfactually for XAI: A Use Case, Algorithm and User Study for Group-Counterfactuals](https://mlsanity.com/paper/2303.09297/) (2023)
- ["How to make them stay?" -- Diverse Counterfactual Explanations of Employee Attrition](https://mlsanity.com/paper/2303.04579/) (2023)

## Built on by (most cited first, 5 of 5)

- [Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels](https://mlsanity.com/paper/2405.17642/) (2024)
- [Explaining Concept Drift through the Evolution of Group Counterfactuals](https://mlsanity.com/paper/2509.09616/) (2025)
- [Fair Recourse for All: Ensuring Individual and Group Fairness in Counterfactual Explanations](https://mlsanity.com/paper/2601.20449/) (2026)
- [DISCOVER: A Solver for Distributional Counterfactual Explanations](https://mlsanity.com/paper/2603.16436/) (2026)
- [Optimal Transport Group Counterfactual Explanations](https://mlsanity.com/paper/2601.20692/) (2026)

## Abstract (arXiv)

Counterfactual explanations constitute among the most popular methods for analyzing black-box systems since they can recommend cost-efficient and actionable changes to the input of a system to obtain the desired system output. While most of the existing counterfactual methods explain a single instance, several real-world problems, such as customer satisfaction, require the identification of a single counterfactual that can satisfy multiple instances (e.g. customers) simultaneously. To address this limitation, in this work, we propose a flexible two-stage algorithm for finding groups of instances and computing cost-efficient multi-instance counterfactual explanations. The paper presents the algorithm and its performance against popular alternatives through a comparative evaluation.