KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929677650624512 |
|---|---|
| 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 |