KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions

TL;DR

KernelSHAP-IQ extends the KernelSHAP method to accurately approximate higher-order Shapley interactions using a weighted least-squares framework, enabling better interpretation of complex ML models.

Contribution

The paper characterizes higher-order Shapley Interaction Index as a solution to a weighted least-squares problem and introduces KernelSHAP-IQ for improved interaction explanations.

Findings

State-of-the-art performance in feature interaction detection

Empirical validation of higher-order SII approximation

Theoretical characterization of SII as WLS solution

Abstract

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.