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

Fuente: arXiv
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Main Authors: Fumagalli, Fabian, Muschalik, Maximilian, Kolpaczki, Patrick, Hüllermeier, Eyke, Hammer, Barbara
Format: Preprint
Published: 2024
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author Fumagalli, Fabian
Muschalik, Maximilian
Kolpaczki, Patrick
Hüllermeier, Eyke
Hammer, Barbara
author_facet Fumagalli, Fabian
Muschalik, Maximilian
Kolpaczki, Patrick
Hüllermeier, Eyke
Hammer, Barbara
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_10852
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions
Fumagalli, Fabian
Muschalik, Maximilian
Kolpaczki, Patrick
Hüllermeier, Eyke
Hammer, Barbara
Machine Learning
Artificial Intelligence
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.
title KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2405.10852