| Presentation | 1995/7/27 On the estimation and prediction error of functional representation with orthnormal discrete variable basis in regression models Taichi Hayasaka, Katsuyuki Hagiwara, Naohiro Toda, Shiro Usui, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | 3-layered neural network models are represented by functions of the form consisting of linear combinations of basis, which can be selected by modifying nonlinearly associated parameters so as to minimize the squared error. In this paper, we pay attention to these properties and deal with the functional representations with orthnormal basis modified by the associated discrete parameters. For such functional representations, we obtain the asymptotic expectations of the least squared error and the squared prediction error with respect to the sample distribution by using extreme value theory. Furthermore, we show that the asymptotic distributions of the absolute values of coefficients are double exponential. These results suggest that we cannot apply the classical theory for linear regression models supposing asymptotic normality of the parameters to the case of the functional representations with variable basis. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | functional representation with discrete variable basis / regression model / squared error / extreme value theory / double exponential distribution |
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| Committee | NC |
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| Conference Date | 1995/7/27(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Neurocomputing (NC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On the estimation and prediction error of functional representation with orthnormal discrete variable basis in regression models |
| Sub Title (in English) | |
| Keyword(1) | functional representation with discrete variable basis |
| Keyword(2) | regression model |
| Keyword(3) | squared error |
| Keyword(4) | extreme value theory |
| Keyword(5) | double exponential distribution |
| 1st Author's Name | Taichi Hayasaka |
| 1st Author's Affiliation | Department of Information and Computer Sciences, Toyohashi University of Technology() |
| 2nd Author's Name | Katsuyuki Hagiwara |
| 2nd Author's Affiliation | Faculty of Engineering, Mie University |
| 3rd Author's Name | Naohiro Toda |
| 3rd Author's Affiliation | Department of Information and Computer Sciences, Toyohashi University of Technology |
| 4th Author's Name | Shiro Usui |
| 4th Author's Affiliation | Department of Information and Computer Sciences, Toyohashi University of Technology |
| Date | 1995/7/27 |
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| Volume (vol) | vol.95 |
| Number (no) | 189 |
| Page | pp.pp.- |
| #Pages | 8 |
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