Quantile Regression with Gaussian Kernels

Baobin Wang; Ting Hu; Hong Yin

doi:10.1007/978-3-030-46161-4_24

Quantile Regression with Gaussian Kernels

Baobin Wang
, Ting Hu
, Hong Yin

South-Central University for Nationalities
Wuhan University
Renmin University of China

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying ε-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.

Original language	English
Title of host publication	Contemporary Experimental Design, Multivariate Analysis and Data Mining
Subtitle of host publication	Festschrift in Honour of Professor Kai-Tai Fang
Publisher	Springer International Publishing
Pages	373-386
Number of pages	14
ISBN (Electronic)	9783030461614
ISBN (Print)	9783030461607
DOIs	https://doi.org/10.1007/978-3-030-46161-4_24
State	Published - 1 Jan 2020
Externally published	Yes

Keywords

Gaussian kernels
Insensitive pinball loss
Learning rate
Quantile regresion
Reproducing kernel Hilbert spaces

Access to Document

10.1007/978-3-030-46161-4_24

Cite this

@inbook{7f1b6c60894048359c70b00932ab62b7,

title = "Quantile Regression with Gaussian Kernels",

abstract = "This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying ε-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.",

keywords = "Gaussian kernels, Insensitive pinball loss, Learning rate, Quantile regresion, Reproducing kernel Hilbert spaces",

author = "Baobin Wang and Ting Hu and Hong Yin",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/978-3-030-46161-4\_24",

language = "英语",

isbn = "9783030461607",

pages = "373--386",

booktitle = "Contemporary Experimental Design, Multivariate Analysis and Data Mining",

publisher = "Springer International Publishing",

}

TY - CHAP

T1 - Quantile Regression with Gaussian Kernels

AU - Wang, Baobin

AU - Hu, Ting

AU - Yin, Hong

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying ε-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.

AB - This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying ε-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.

KW - Gaussian kernels

KW - Insensitive pinball loss

KW - Learning rate

KW - Quantile regresion

KW - Reproducing kernel Hilbert spaces

UR - https://www.scopus.com/pages/publications/85150117025

U2 - 10.1007/978-3-030-46161-4_24

DO - 10.1007/978-3-030-46161-4_24

M3 - 章节

AN - SCOPUS:85150117025

SN - 9783030461607

SP - 373

EP - 386

BT - Contemporary Experimental Design, Multivariate Analysis and Data Mining

PB - Springer International Publishing

ER -

Quantile Regression with Gaussian Kernels

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this