Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature importance scores for any black box model. Shapley interaction indices extend the SV to define any-order feature interaction scores. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

翻译：在可解释人工智能（XAI）研究中，Shapley值（SV）主要用于确定任何黑箱模型的特征重要性得分。Shapley交互作用指数将SV扩展至任意阶特征交互作用的评分。定义唯一的Shapley交互作用指数是一项开放研究问题，目前已有三种基于不同公理选择的定义，且每种定义需要特定的逼近技术。本文提出SHapley交互作用量化方法（SHAP-IQ），一种基于采样的高效逼近器，用于计算任意基数交互作用指数（CII）的Shapley交互作用，即满足线性性、对称性和哑元公理条件的交互作用指数。SHAP-IQ基于一种新的表示方法，与现有方法相比，我们为其逼近质量提供了理论保证，并给出了点估计方差的估计值。在SV的特殊情形下，我们的方法揭示了SV的一种新表示，并对应于计算极大简化的无偏KernelSHAP。我们通过解释语言模型、图像分类模型及高维合成模型，展示了该方法的计算效率与有效性。