KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions
<|reference_start|>KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley 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.<|reference_end|>
@article{fumagalli2024kernelshap-iq:,
    title={KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley
  Interactions},
    author={Fabian Fumagalli, Maximilian Muschalik, Patrick Kolpaczki, Eyke
  H"ullermeier, Barbara Hammer},
    journal={arXiv preprint arXiv:2405.10852},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.10852},
    primaryClass={cs.LG cs.AI}
}