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Learning Rates for Kernel-Based Expectile Regression

Muhammad Farooq, Ingo Steinwart

Machine Learning, 108, pp. 203–227, 2019.


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.



@article{farooq19_ml, author = {Farooq, Muhammad and Steinwart, Ingo}, title = {Learning Rates for Kernel-Based Expectile Regression}, year = {2019}, volume = {108}, pages = {203--227}, journal = {Machine Learning}, preprint = {https://arxiv.org/abs/1702.07552}, doi = {10.1007/s10994-018-5762-9} }