Presentation	2015-03-05 Soft-thresholding with scaling for non-parametric orthogonal regression problem Katsuyuki HAGIWARA,
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Abstract(in English)	In this paper, we introduced a positive scaling for soft-thresholding estimators in a non-parametric orthogonal regression problem. Under LARS (least angle regression) based soft-thresholding, we first gave a risk (generalization error) for a fixed scaling. We then showed that an optimal scaling value that minimizes the risk under a sparseness condition is 1+O(√), where n is the number of samples. The important point is that the optimal value of scaling is larger than one. This implies that expanding soft-thresholding estimator shows a better generalization performance compared to a naive soft-thresholding and elastic net that yields shrinkage of soft-thresholding. This also implies that a risk of LARS-oriented soft-thresholding with the optimal scaling is smaller than without scaling, for which we showed their difference is O(log n/n).
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Keyword(in English)	non-parametric orthogonal regression / soft-thresholding / shrinkage / scaling / LASSO
Paper #	IBISML2014-88
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Committee	IBISML
Conference Date	2015/2/26(1days)
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Paper Information
Registration To	Information-Based Induction Sciences and Machine Learning (IBISML)
Language	ENG
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Soft-thresholding with scaling for non-parametric orthogonal regression problem
Sub Title (in English)
Keyword(1)	non-parametric orthogonal regression
Keyword(2)	soft-thresholding
Keyword(3)	shrinkage
Keyword(4)	scaling
Keyword(5)	LASSO
1st Author's Name	Katsuyuki HAGIWARA
1st Author's Affiliation	Faculty of Education, Mie University()
Date	2015-03-05
Paper #	IBISML2014-88
Volume (vol)	vol.114
Number (no)	502
Page	pp.pp.-
#Pages	8
Date of Issue