  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.
