| Presentation | 2007-03-14 Estimation of poles of zeta function in learning theory using pade approximation Ryosuke IRIGUCHI, Sumio WATANABE, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Learning machines such as neural networks, Gaussian mixtures, Bayes networks, hidden Markov models, and Boltzmann machines are called singular learning machines, which have been applied to many real problems such as pattern recognition, time-series prediction, and system control. However, these learning machines have singular points which are attributable to their hierarchical structures or symmetry property. Hence, the maximum likelihood estimators do not have asymptotic normality, and conventional asymptotic theory for statistical regular models can not be applied. Therefore, theoretical optimum model selections or designs involve algebraic geometrical analysis. The algebraic geometrical analysis requires blowing up, which is to obtain maximum poles of zeta functions in learning theory, however, it is hard for complex learning machines. In this paper, a new method which obtains the maximum poles of zeta functions in learning theory by numerical computations is proposed. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Singular Learning Machine / Beyes Learning / Learning Coefficient / Zeta Function / Fade Approximation |
| Paper # | NC2006-135 |
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| Committee | NC |
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| Conference Date | 2007/3/7(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) | Estimation of poles of zeta function in learning theory using pade approximation |
| Sub Title (in English) | |
| Keyword(1) | Singular Learning Machine |
| Keyword(2) | Beyes Learning |
| Keyword(3) | Learning Coefficient |
| Keyword(4) | Zeta Function |
| Keyword(5) | Fade Approximation |
| 1st Author's Name | Ryosuke IRIGUCHI |
| 1st Author's Affiliation | Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology() |
| 2nd Author's Name | Sumio WATANABE |
| 2nd Author's Affiliation | Precision and intelligence Laboratory, Tokyo Institute of Technology |
| Date | 2007-03-14 |
| Paper # | NC2006-135 |
| Volume (vol) | vol.106 |
| Number (no) | 588 |
| Page | pp.pp.- |
| #Pages | 6 |
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