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Paper Abstract and Keywords
Presentation 2014-11-18 15:00
[Poster Presentation] A note on least angle regression in orthogonal case
Katsuyuki Hagiwara (Mie Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) LARS(least angle regression) is one of the sparse modeling methods. This paper considered LARS in the case of orthogonal design matrix, which we refer to as LARSO(LARS in the Orthogonal case). LARSO is not only an example
for understanding LARS but also is important in applications especially in the context of non-parametric regression including wavelet denoising. In this paper, we showed that LARSO is represented by a simple non-iterative algorithm. Interestingly, the resulting estimators of coefficients are shrinkage estimators under a greedy procedure. Based on this result, we found that
LARSO is exactly equivalent to a soft-thresholding method in which a threshold level at the kth step is the (k + 1)th largest absolute value of the least squares estimators. We also gave a simple proof of deriving a Cp type model selection criterion for LARSO. It is interpreted as a criterion not only for choosing the number of steps/coefficients of LARSO but also for determining an optimal threshold level in LARSO-oriented soft-thresholding method. Furthermore, in the context of non-parametric regression, we clarified relationship between LARSO and several methods such as the universal thresholding and SUREshrink in wavelet denoising. Throughout numerical experiments of application to wavelet denoising, we showed that LARSO with Cp type criterion outperforms the universal soft-thresholding method in terms of a generalization performance.
Keyword (in Japanese) (See Japanese page) 
(in English) LARS / 直交回帰 / soft-thresholding / wavelet denoising / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 306, IBISML2014-61, pp. 199-206, Nov. 2014.
Paper # IBISML2014-61 
Date of Issue 2014-11-10 (IBISML) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380

Conference Information
Committee IBISML  
Conference Date 2014-11-17 - 2014-11-19 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagoya Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IBISML 
Conference Code 2014-11-IBISML 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A note on least angle regression in orthogonal case 
Sub Title (in English)  
Keyword(1) LARS  
Keyword(2) 直交回帰  
Keyword(3) soft-thresholding  
Keyword(4) wavelet denoising  
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1st Author's Name Katsuyuki Hagiwara  
1st Author's Affiliation Mie University (Mie Univ.)
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Speaker
Date Time 2014-11-18 15:00:00 
Presentation Time 180 
Registration for IBISML 
Paper # IEICE-IBISML2014-61 
Volume (vol) IEICE-114 
Number (no) no.306 
Page pp.199-206 
#Pages IEICE-8 
Date of Issue IEICE-IBISML-2014-11-10 


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