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Quantile Regression with Gaussian Kernels

In: Contemporary Experimental Design, Multivariate Analysis and Data Mining

Author

Listed:
  • Baobin Wang

    (South-Central University for Nationalities, School of Mathematics and Statistics)

  • Ting Hu

    (Wuhan University, School of Mathematics and Statistics)

  • Hong Yin

    (Renmin University of China, School of Mathematics)

Abstract

This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying $$\epsilon $$-insensitive pinball loss functions and flexible Gaussian kernels. Analyzing sparsity and learning rates will be provided when the target function lies in some Sobolev spaces and a noise condition is satisfied for the underlying probability measure. Our results show that selecting the variance of the Gaussian kernel plays a crucial role in the learning performance of quantile regression algorithms.

Suggested Citation

  • Baobin Wang & Ting Hu & Hong Yin, 2020. "Quantile Regression with Gaussian Kernels," Springer Books, in: Jianqing Fan & Jianxin Pan (ed.), Contemporary Experimental Design, Multivariate Analysis and Data Mining, chapter 0, pages 373-386, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46161-4_24
    DOI: 10.1007/978-3-030-46161-4_24
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