| Presentation | 2014-11-18 A note on least angle regression in orthogonal case Katsuyuki HAGIWARA, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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 C_p 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 C_p type criterion outperforms the universal soft-thresholding method in terms of a generalization performance. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | LARS / orthogonal regression / soft-thresholding / wavelet denoising |
| Paper # | IBISML2014-61 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2014/11/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Information-Based Induction Sciences and Machine Learning (IBISML) |
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| Language | ENG |
| 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) | orthogonal regression |
| Keyword(3) | soft-thresholding |
| Keyword(4) | wavelet denoising |
| 1st Author's Name | Katsuyuki HAGIWARA |
| 1st Author's Affiliation | Faculty of Education, Mie University() |
| Date | 2014-11-18 |
| Paper # | IBISML2014-61 |
| Volume (vol) | vol.114 |
| Number (no) | 306 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |