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Main Authors: Tang, Qian, Gu, Yuwen, Wang, Boxiang
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2408.05393
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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