We present PPCEF, a novel method for generating probabilistically plausible
counterfactual explanations (CFs). PPCEF advances beyond existing methods by
combining a probabilistic formulation that leverages the data distribution with
the optimization of plausibility within a unified framework. Compared to
reference approaches, our method enforces plausibility by directly optimizing
the explicit density function without assuming a particular family of
parametrized distributions. This ensures CFs are not only valid (i.e., achieve
class change) but also align with the underlying data's probability density.
For that purpose, our approach leverages normalizing flows as powerful density
estimators to capture the complex high-dimensional data distribution.
Furthermore, we introduce a novel loss that balances the trade-off between
achieving class change and maintaining closeness to the original instance while
also incorporating a probabilistic plausibility term. PPCEF's unconstrained
formulation allows for efficient gradient-based optimization with batch
processing, leading to orders of magnitude faster computation compared to prior
methods. Moreover, the unconstrained formulation of PPCEF allows for the
seamless integration of future constraints tailored to specific counterfactual
properties. Finally, extensive evaluations demonstrate PPCEF's superiority in
generating high-quality, probabilistically plausible counterfactual
explanations in high-dimensional tabular settings. This makes PPCEF a powerful
tool for not only interpreting complex machine learning models but also for
improving fairness, accountability, and trust in AI systems.

我们提出了 PPCEF，一种用于生成概率上可信的反事实解释（CFs）的新方法。PPCEF 通过将概率形式与在一个统一框架内优化可信度相结合，超越了现有方法。与参考方法相比，我们的方法通过直接优化显式密度函数而不假定特定的参数化分布家族来强制执行可信度。这确保了 CFs 不仅是有效的（即实现了类别变化），而且与底层数据的概率密度相一致。为此，我们的方法利用规范化流作为强大的密度估计器来捕捉复杂的高维数据分布。此外，我们引入了一种新颖的损失函数，平衡了实现类别变化和保持与原始实例的相似性之间的权衡，并结合了概率可信度项。PPCEF 的无约束形式允许有效的基于梯度的批处理优化，与之前的方法相比，计算速度提高了几个数量级。此外，PPCEF 的无约束形式允许将来的约束无缝集成，以符合特定的反事实属性。最后，广泛的评估证明了 PPCEF 在生成高质量、概率上可信的高维表格设置中的反事实解释方面的优势。这使得 PPCEF 不仅成为解释复杂机器学习模型的强大工具，而且提高了 AI 系统的公平性、问责制和信任度。