In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques. Code is available at https://github.com/trusty-ai/efficient-consistent-explanations.

翻译：在当前的解释方法学领域，主流方法（如SHAP和LIME）通过模拟特定特征被省略的各种场景，采用基于删除的技术来评估单个特征的影响。然而，这些方法主要侧重于原始上下文中的效率，往往导致普遍的不一致性。本文通过建立“不可能三角定理”证明这种不一致性是这些方法的固有特征，该定理指出可解释性、效率和一致性无法同时实现。鉴于理想解释的达成仍然难以企及，我们提出将解释误差作为衡量低效与不一致性的指标。为此，我们提出两种基于标准多项式基的新算法，旨在最小化解释误差。实验结果表明，与替代技术相比，所提方法在解释误差上实现了显著降低，最高可达31.8倍。代码已开源在https://github.com/trusty-ai/efficient-consistent-explanations。