The Shapley value (SV) is a prevalent approach of allocating credit to machine learning (ML) entities to understand black box ML models. Enriching such interpretations with higher-order interactions is inevitable for complex systems, where the Shapley Interaction Index (SII) is a direct axiomatic extension of the SV. While it is well-known that the SV yields an optimal approximation of any game via a weighted least square (WLS) objective, an extension of this result to SII has been a long-standing open problem, which even led to the proposal of an alternative index. In this work, we characterize higher-order SII as a solution to a WLS problem, which constructs an optimal approximation via SII and $k$-Shapley values ($k$-SII). We prove this representation for the SV and pairwise SII and give empirically validated conjectures for higher orders. As a result, we propose KernelSHAP-IQ, a direct extension of KernelSHAP for SII, and demonstrate state-of-the-art performance for feature interactions.

该研究论文提出了一种对机器学习模型进行解释的方法，通过使用Shapley value（沙普利价值）和Shapley Interaction Index（沙普利相互作用指数）来分析黑盒机器学习模型中的信用分配问题，并且给出了一种称为KernelSHAP-IQ的方法来解决特征相互作用的问题。

KernelSHAP-IQ: Shapley交互的加权最小二乘优化