# fastkqr: A Fast Algorithm for Kernel Quantile Regression

arXiv: https://arxiv.org/abs/2408.05393 · HTML: https://mlsanity.com/paper/2408.05393/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 10 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [Smoothing quantile regressions](https://mlsanity.com/paper/1905.08535/) (2019)
- [High-Dimensional Quantile Regression: Convolution Smoothing and Concave Regularization](https://mlsanity.com/paper/2109.05640/) (2021)
- [Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression](https://mlsanity.com/paper/1509.02957/) (2015)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Extremal Quantile Regression: An Overview](https://mlsanity.com/paper/1612.06850/) (2016)

## Built on by (most cited first, 1 of 1)

- [TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection](https://mlsanity.com/paper/2606.06742/) (2026)

## Abstract (arXiv)

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.