# Optimal Transport Group Counterfactual Explanations

arXiv: https://arxiv.org/abs/2601.20692 · HTML: https://mlsanity.com/paper/2601.20692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## 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)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [Global Counterfactual Explanations: Investigations, Implementations and Improvements](https://mlsanity.com/paper/2204.06917/) (2022)
- [Generating collective counterfactual explanations in score-based classification via mathematical optimization](https://mlsanity.com/paper/2310.12822/) (2023)
- [A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations](https://mlsanity.com/paper/2403.01221/) (2024)
- [Unifying Perspectives: Plausible Counterfactual Explanations on Global, Group-wise, and Local Levels](https://mlsanity.com/paper/2405.17642/) (2024)
- [FACEGroup: Feasible and Actionable Counterfactual Explanations for Group Fairness](https://mlsanity.com/paper/2410.22591/) (2024)
- [Actionable Counterfactual Explanations Using Bayesian Networks and Path Planning with Applications to Environmental Quality Improvement](https://mlsanity.com/paper/2508.02634/) (2025)

## Abstract (arXiv)

Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively. However, existing methods either (i) optimize counterfactuals only for a fixed group and do not generalize to new group members, (ii) strictly rely on strong model assumptions (e.g., linearity) for tractability or/and (iii) poorly control the counterfactual group geometry distortion. We instead learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization, minimizing the group's total transport cost. This enables generalization with fewer parameters, making it easier to interpret the common actionable recourse. For linear classifiers, we prove that functions representing group counterfactuals are derived via mathematical optimization, identifying the underlying convex optimization type (QP, QCQP, ...). Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost compared to baseline methods. If model linearity cannot be exploited, our approach also significantly outperforms the baselines.