Efficient Shapley Performance Attribution for Least-Squares Regression
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arXiv
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| Format: | Preprint |
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2023
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| author | Bell, Logan Devanathan, Nikhil Boyd, Stephen |
| author_facet | Bell, Logan Devanathan, Nikhil Boyd, Stephen |
| contents | We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving a number of regression problems that is exponential in the number of features, so a Monte Carlo-type approximation is typically used. We focus on the special case of least-squares regression models, where several tricks can be used to compute and evaluate regression models efficiently. These tricks give a substantial speed up, allowing many more Monte Carlo samples to be evaluated, achieving better accuracy. We refer to our method as least-squares Shapley performance attribution (LS-SPA), and describe our open-source implementation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_19245 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Shapley Performance Attribution for Least-Squares Regression Bell, Logan Devanathan, Nikhil Boyd, Stephen Computation 62-08 (Primary), 62-04, 62J99 (Secondary) We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving a number of regression problems that is exponential in the number of features, so a Monte Carlo-type approximation is typically used. We focus on the special case of least-squares regression models, where several tricks can be used to compute and evaluate regression models efficiently. These tricks give a substantial speed up, allowing many more Monte Carlo samples to be evaluated, achieving better accuracy. We refer to our method as least-squares Shapley performance attribution (LS-SPA), and describe our open-source implementation. |
| title | Efficient Shapley Performance Attribution for Least-Squares Regression |
| topic | Computation 62-08 (Primary), 62-04, 62J99 (Secondary) |
| url | https://arxiv.org/abs/2310.19245 |