Counterfactual Explanations (CE) face several unresolved challenges, such as ensuring stability, synthesizing multiple CEs, and providing plausibility and sparsity guarantees. From a more practical point of view, recent studies [Pawelczyk et al., 2022] show that the prescribed counterfactual recourses are often not implemented exactly by individuals and demonstrate that most state-of-the-art CE algorithms are very likely to fail in this noisy environment. To address these issues, we propose a probabilistic framework that gives a sparse local counterfactual rule for each observation, providing rules that give a range of values capable of changing decisions with high probability. These rules serve as a summary of diverse counterfactual explanations and yield robust recourses. We further aggregate these local rules into a regional counterfactual rule, identifying shared recourses for subgroups of the data. Our local and regional rules are derived from the Random Forest algorithm, which offers statistical guarantees and fidelity to data distribution by selecting recourses in high-density regions. Moreover, our rules are sparse as we first select the smallest set of variables having a high probability of changing the decision. We have conducted experiments to validate the effectiveness of our counterfactual rules in comparison to standard CE and recent similar attempts. Our methods are available as a Python package.

翻译：反事实解释面临若干未解决的挑战，例如确保稳定性、综合多个反事实解释、以及提供合理性和稀疏性保证。从更实际的角度来看，近期研究 [Pawelczyk 等，2022] 表明，所指定的反事实应对措施往往无法被个体完全执行，并证明大多数最先进的反事实解释算法在此噪声环境下极可能失效。为解决这些问题，我们提出一个概率框架，为每个观测值生成稀疏的局部反事实规则，这些规则提供能够以高概率改变决策的值域范围。这些规则作为多样化反事实解释的总结，并产生稳健的应对措施。我们进一步将这些局部规则聚合为区域反事实规则，识别数据子组的共享应对措施。我们的局部与区域规则基于随机森林算法推导而来，该算法通过在高密度区域选择应对措施，提供统计保证并保持与数据分布的一致性。此外，由于我们首先选取具有高概率改变决策的最小变量集合，因此规则具有稀疏性。我们通过实验验证了反事实规则相较于标准反事实解释及近期类似方法的有效性。我们的方法已作为 Python 包发布。