KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions
This work addresses the need for more interpretable machine learning models by providing a method to compute higher-order interactions, which is incremental as it builds on existing Shapley value techniques.
The paper tackles the problem of extending the Shapley value to higher-order interactions for interpreting black-box machine learning models, by characterizing the Shapley Interaction Index as a solution to a weighted least-square optimization problem and proposing KernelSHAP-IQ, which achieves state-of-the-art performance for feature interactions.
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.