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 inconsistencies and inefficiencies. 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.

翻译：在当前解释方法学的研究格局中，主流方法如SHAP和LIME通常采用基于移除的技术，通过模拟特定特征被省略的各种场景来评估单个特征的影响。然而，这些方法主要侧重于原始情境下的效率，往往导致普遍的不一致性。本文通过建立“不可能三角定理”证明了这种不一致性是这些方法的固有特性，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实现，我们提出将解释误差作为衡量不一致性和低效率的指标。为此，我们提出了两种基于标准多项式基的新算法，旨在最小化解误差。我们的实证结果表明，所提方法在解误差上实现了显著降低，相较于其他技术最多可降低31.8倍。