fastkqr: A Fast Algorithm for Kernel Quantile Regression
<|reference_start|>fastkqr: A Fast Algorithm for Kernel Quantile Regression: 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.<|reference_end|>
@article{tang2024fastkqr:,
    title={fastkqr: A Fast Algorithm for Kernel Quantile Regression},
    author={Qian Tang, Yuwen Gu, Boxiang Wang},
    journal={arXiv preprint arXiv:2408.05393},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.05393},
    primaryClass={stat.ML cs.LG}
}