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fastkqr: A Fast Algorithm for Kernel Quantile Regression
Preprint   Open access

fastkqr: A Fast Algorithm for Kernel Quantile Regression

Qian Tang, Yuwen Gu and Boxiang Wang
ArXiv.org
Cornell University
08/10/2024
DOI: 10.48550/arxiv.2408.05393
url
https://doi.org/10.48550/arxiv.2408.05393View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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.
Computer Science - Learning Statistics - Machine Learning

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