Learning Rates for Kernel-Based Expectile Regression
Muhammad Farooq, Ingo Steinwart
Machine Learning, 108, pp. 203–227, 2019.
Abstract
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are used and the desired expectile is smooth in a Besov sense. As a special case, our learning rates improves the best known rates for kernel-based least squares regression in aforementioned scenario. Key ingredients of our statistical analysis are a general calibration inequality for the asymmetric least squares loss, a corresponding variance bound as well as an improved entropy number bound for Gaussian RBF kernels.Links
BibTeX
@article{farooq19_ml,
title = {Learning Rates for Kernel-Based Expectile Regression},
author = {Farooq, Muhammad and Steinwart, Ingo},
year = {2019},
journal = {Machine Learning},
volume = {108},
pages = {203--227},
doi = {10.1007/s10994-018-5762-9}
}