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.

翻译：群体反事实解释旨在通过寻找一组反事实实例来对比性地解释一组输入实例。然而，现有方法要么（i）仅针对固定群体优化反事实，无法泛化到新的群体成员；要么（ii）为保持可处理性而严格依赖强模型假设（如线性）；和/或（iii）对反事实群体几何形变的控制能力较差。我们转而学习一个显式的最优传输映射，该映射可将任意群体实例直接发送至其反事实结果而无需重新优化，从而最小化群体的总传输成本。这能以更少的参数实现泛化，使共同可操作的补救措施更易于解释。对于线性分类器，我们证明了表征群体反事实的函数可通过数学优化推导得出，并识别了其背后的凸优化类型（QP、QCQP等）。实验表明，这些方法能准确泛化，保持群体几何结构，且相较于基线方法仅产生可忽略的额外传输成本。若无法利用模型线性特性，我们的方法同样显著优于基线。