When: Friday, March 22, from 2:00 PM to 3:00 PM Where: ENGR 045
Abstract: Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. Its broader application, however, is often hindered by the substantial computational demands arising from the nonsmooth quantile loss function. We introduce a novel algorithm named fastkqr, which significantly advances the computation of quantile regression in reproducing kernel Hilbert spaces. The crux 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 an innovative spectral technique that carefully reuses matrix computations. In addition, we extend fastkqr to solve a flexible kernel quantile regression with a data-driven crossing penalty. The new method addresses the interpretability issue with quantile regression where fitted quantile curves at multiple levels are often crossing in a finite sample. Extensive simulations and real applications show that fastkqr achieves the same accuracy as the state-of-the-art algorithms but can be an order of magnitude faster.