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Gradient-based kernel dimension reduction for regression
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Fukumizu, Kenji and Leng, Chenlei (2014) Gradient-based kernel dimension reduction for regression. Journal of the American Statistical Association, Volume 109 (Number 505). pp. 359-370. doi:10.1080/01621459.2013.838167 ISSN 0162-1459.
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Official URL: http://dx.doi.org/10.1080/01621459.2013.838167
Abstract
This article proposes a novel approach to linear dimension reduction for regression using nonparametric estimation with positive-definite kernels or reproducing kernel Hilbert spaces (RKHSs). The purpose of the dimension reduction is to find such directions in the explanatory variables that explain the response sufficiently: this is called sufficient dimension reduction. The proposed method is based on an estimator for the gradient of the regression function considered for the feature vectors mapped into RKHSs. It is proved that the method is able to estimate the directions that achieve sufficient dimension reduction. In comparison with other existing methods, the proposed one has wide applicability without strong assumptions on the distributions or the type of variables, and needs only Eigen decomposition for estimating the projection matrix. The theoretical analysis shows that the estimator is consistent with certain rate under some conditions. The experimental results demonstrate that the proposed method successfully finds effective directions with efficient computation even for high-dimensional explanatory variables.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Journal of the American Statistical Association | ||||||||
Publisher: | Taylor Francis | ||||||||
ISSN: | 0162-1459 | ||||||||
Official Date: | 19 March 2014 | ||||||||
Dates: |
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Volume: | Volume 109 | ||||||||
Number: | Number 505 | ||||||||
Number of Pages: | 11 | ||||||||
Page Range: | pp. 359-370 | ||||||||
DOI: | 10.1080/01621459.2013.838167 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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