fastkqr: A Fast Algorithm for Kernel Quantile Regression
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912533662662656 |
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| author | Tang, Qian Gu, Yuwen Wang, Boxiang |
| author_facet | Tang, Qian Gu, Yuwen Wang, Boxiang |
| contents | Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising from the non-smooth quantile loss function. In this paper, we introduce a novel algorithm named fastkqr, which significantly advances the computation of quantile regression in reproducing kernel Hilbert spaces. The core of fastkqr is a finite smoothing algorithm that magically produces exact regression quantiles, rather than approximations. To further accelerate the algorithm, we equip fastkqr with a novel spectral technique that carefully reutilizes matrix computations. In addition, we extend fastkqr to accommodate a flexible kernel quantile regression with a data-driven crossing penalty, addressing the interpretability challenges of crossing quantile curves at multiple levels. We have implemented fastkqr in a publicly available R package. Extensive simulations and real applications show that fastkqr matches the accuracy of state-of-the-art algorithms but can operate up to an order of magnitude faster. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | fastkqr: A Fast Algorithm for Kernel Quantile Regression Tang, Qian Gu, Yuwen Wang, Boxiang Machine Learning Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising from the non-smooth quantile loss function. In this paper, we introduce a novel algorithm named fastkqr, which significantly advances the computation of quantile regression in reproducing kernel Hilbert spaces. The core of fastkqr is a finite smoothing algorithm that magically produces exact regression quantiles, rather than approximations. To further accelerate the algorithm, we equip fastkqr with a novel spectral technique that carefully reutilizes matrix computations. In addition, we extend fastkqr to accommodate a flexible kernel quantile regression with a data-driven crossing penalty, addressing the interpretability challenges of crossing quantile curves at multiple levels. We have implemented fastkqr in a publicly available R package. Extensive simulations and real applications show that fastkqr matches the accuracy of state-of-the-art algorithms but can operate up to an order of magnitude faster. |
| title | fastkqr: A Fast Algorithm for Kernel Quantile Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2408.05393 |