fastkqr: A Fast Algorithm for Kernel Quantile Regression

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Quantile regression is valuable for robust and heterogeneous learning.
• Computational demands of quantile regression hinder its application.
• Existing methods struggle with non-smooth quantile loss functions.

Purpose of the Study:

• Introduce fastkqr, a novel algorithm for efficient computation of quantile regression.
• Advance the application of quantile regression in reproducing kernel Hilbert spaces.
• Address challenges in kernel quantile regression, including interpretability.

Main Methods:

• Developed fastkqr utilizing a finite smoothing algorithm for exact quantile computation.
• Incorporated a spectral technique to accelerate matrix computations.
• Extended fastkqr with a data-driven crossing penalty for flexible kernel quantile regression.

Main Results:

• fastkqr achieves exact regression quantiles without approximation.
• The algorithm demonstrates significant speed improvements, up to an order of magnitude faster.
• The extended version handles crossing quantile curves effectively.

Conclusions:

• fastkqr offers a computationally efficient and accurate solution for quantile regression.
• The algorithm enhances the practical applicability of robust and heterogeneous learning.
• A publicly available R package facilitates the use of fastkqr.