Learning Rates for Kernel-Based Expectile Regression

Muhammad Farooq; Ingo Steinwart

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arXiv · 1702.07552

Learning Rates for Kernel-Based Expectile Regression

Muhammad Farooq·Ingo Steinwart

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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 improve the best known rates for kernel-based least squares regression in this 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.

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BibTeX RIS

Muhammad Farooq, Ingo Steinwart. 2017-02-24. Learning Rates for Kernel-Based Expectile Regression. https://arxiv.org/abs/1702.07552

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