| Presentation | 2002/10/10 Algebraic Geometry of Complete Bipartite Graph-type Boltzmann Machines Keisuke YAMAZAKI, Sumio WATANABE, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | It is well known that Boltzmann machines are non-regular statistical models. The set of their parameters of small size models is an analystic set with singularities in the space of a large size ones. The mathematical foundation of their learning is not yet constructed because of the singularities, though they are applied in many situations of information engineering. Recently we established the method to calculate the bayes generalization errors with an algebraic geometric method even if the models are non-regular. This paper shows that the upper bounds of generalization errors in Boltzmann machines is smaller than the ones in regular statistical models. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Boltzmann machine / Generalization error / Algebraic Geometry |
| Paper # | NC2002-53 |
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| Committee | NC |
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| Conference Date | 2002/10/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Neurocomputing (NC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Algebraic Geometry of Complete Bipartite Graph-type Boltzmann Machines |
| Sub Title (in English) | |
| Keyword(1) | Boltzmann machine |
| Keyword(2) | Generalization error |
| Keyword(3) | Algebraic Geometry |
| 1st Author's Name | Keisuke YAMAZAKI |
| 1st Author's Affiliation | Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology() |
| 2nd Author's Name | Sumio WATANABE |
| 2nd Author's Affiliation | Precidion and Intelligence Laboratory, Tokyo Institute of Technology |
| Date | 2002/10/10 |
| Paper # | NC2002-53 |
| Volume (vol) | vol.102 |
| Number (no) | 381 |
| Page | pp.pp.- |
| #Pages | 6 |
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