Fairness Analysis with Shapley-Owen Effects
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929519944794112 |
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| author | Ruess, Harald |
| author_facet | Ruess, Harald |
| contents | We argue that relative importance and its equitable attribution in terms of Shapley-Owen effects is an appropriate one, and, if we accept a small number of reasonable imperatives for equitable attribution, the only way to measure fairness. On the other hand, the computation of Shapley-Owen effects can be very demanding. Our main technical result is a spectral decomposition of the Shapley-Owen effects, which decomposes the computation of these indices into a model-specific and a model-independent part. The model-independent part is precomputed once and for all, and the model-specific computation of Shapley-Owen effects is expressed analytically in terms of the coefficients of the model's \emph{polynomial chaos expansion} (PCE), which can now be reused to compute different Shapley-Owen effects. We also propose an algorithm for computing precise and sparse truncations of the PCE of the model and the spectral decomposition of the Shapley-Owen effects, together with upper bounds on the accumulated approximation errors. The approximations of both the PCE and the Shapley-Owen effects converge to their true values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fairness Analysis with Shapley-Owen Effects Ruess, Harald Artificial Intelligence Computer Science and Game Theory We argue that relative importance and its equitable attribution in terms of Shapley-Owen effects is an appropriate one, and, if we accept a small number of reasonable imperatives for equitable attribution, the only way to measure fairness. On the other hand, the computation of Shapley-Owen effects can be very demanding. Our main technical result is a spectral decomposition of the Shapley-Owen effects, which decomposes the computation of these indices into a model-specific and a model-independent part. The model-independent part is precomputed once and for all, and the model-specific computation of Shapley-Owen effects is expressed analytically in terms of the coefficients of the model's \emph{polynomial chaos expansion} (PCE), which can now be reused to compute different Shapley-Owen effects. We also propose an algorithm for computing precise and sparse truncations of the PCE of the model and the spectral decomposition of the Shapley-Owen effects, together with upper bounds on the accumulated approximation errors. The approximations of both the PCE and the Shapley-Owen effects converge to their true values. |
| title | Fairness Analysis with Shapley-Owen Effects |
| topic | Artificial Intelligence Computer Science and Game Theory |
| url | https://arxiv.org/abs/2409.19318 |