用最优传输方法生成可推广的群体反事实解释，保持群体结构且计算高效。
Optimal Transport Group Counterfactual Explanations
- 构建显式最优传输映射，无需重新优化即可生成新成员的反事实
- 线性分类器下证明反事实函数为凸优化解，类型包括QP、QCQP等
- 实验显示能精准泛化、保持群体几何形状，额外代价极小
群体反事实解释旨在通过一组反事实实例对比解释多个输入实例。现有方法或仅针对固定群体优化而无法推广至新成员，或严格依赖强模型假设（如线性）以保证可计算性，或对群体几何结构扭曲控制不足。本文提出学习一个显式的最优传输映射，将任意群体实例直接映射到其反事实，无需重新优化，并最小化群体总运输成本。该方法实现参数更少的泛化能力，便于解释共同可操作的补救措施。对于线性分类器，我们证明了群体反事实函数可通过数学优化推导得出，确定其对应的凸优化类型（如二次规划QP、二次约束二次规划QCQP等）。实验表明，该方法能准确泛化、有效保持群体几何结构，与基线方法相比仅增加可忽略的额外运输成本；即使无法利用模型线性，仍显著优于基线。
原文摘要 · Abstract (English)
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.
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