| Presentation | 2003/7/21 Resolution of singularities and its application to learning theory Miki AOYAGI, Sumio WATANABE, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Our purpose in this paper is to give an introduction to algebraic geometry and especially construction of the blowing-up. This construction is the main tool in the resolution of singularities of an algebraic variety. By using the blowing-up process, it can be calculated the poles of a zeta function which is the integral of the Kullback distance and a certain priori probability density funciton. Hierarchical learning machines such as layered neural networks and Gaussian mixtures are non-regular learning machines. It was proved that the largest pole of the zeta function asymptotically gives the stochastic complexity of non-regular learning machine (see[1]～[3]). |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | stochastic complexity / layered neural networks / non-regular learning machines / Bayesian estimate / resolution of singularities |
| Paper # | NC2003-26 |
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| Conference Information | |
| Committee | NC |
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| Conference Date | 2003/7/21(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| 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) | Resolution of singularities and its application to learning theory |
| Sub Title (in English) | |
| Keyword(1) | stochastic complexity |
| Keyword(2) | layered neural networks |
| Keyword(3) | non-regular learning machines |
| Keyword(4) | Bayesian estimate |
| Keyword(5) | resolution of singularities |
| 1st Author's Name | Miki AOYAGI |
| 1st Author's Affiliation | Faculty of Science and Technology, Sophia University() |
| 2nd Author's Name | Sumio WATANABE |
| 2nd Author's Affiliation | Precision and Intelligence Laboratory, Tokyo Institute of Technology |
| Date | 2003/7/21 |
| Paper # | NC2003-26 |
| Volume (vol) | vol.103 |
| Number (no) | 227 |
| Page | pp.pp.- |
| #Pages | 6 |
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