Canonical kernel dimension reduction
A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational effic...
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Published in | Computational statistics & data analysis Vol. 107; pp. 131 - 148 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.03.2017
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Subjects | |
Online Access | Get full text |
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Summary: | A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational efficiency. The choice of loss function in cross-validation is discussed, and a two-stage screening procedure is proposed. Empirical evidence shows that the new method yields favorable performance, both in terms of accuracy and scalability, especially for large and more challenging datasets compared with other distribution-free SDR methods.
•A new sufficient dimension reduction method based on kernel canonical functions.•This new method is distribution free and highly scalable.•We give theoretical proof of the sufficient dimension reduction property.•We present efficient algorithms and discuss the choice of loss function.•Extensive experiments demonstrate its advantage over existing approaches. |
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ISSN: | 0167-9473 1872-7352 |
DOI: | 10.1016/j.csda.2016.10.003 |