| Presentation | 2003/7/21 Algebraic Geometry of Stochastic Complexity for Bayesian Networks Keisuke YAMAZAKI, Sumio WATANABE, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Bayesian networks are now used in enormous fields, for example, system diagnosis, data mining, clusterings ets. In spite of wide range of their applications, the statistical properties have not yet been clarified because the models are nonidentifiable and non-regular. In recent years, however, we have developed a method to analyze non-regular models by using algebraic geometry. In this paper, applying this method to Bayesian networks with latent variables, we clarify the orders of the stochastic complexities. Our result shows that their upper bound is smaller than the dimension of the parameter space. This means that the Bayesian generalization error is also far smaller than that of a regular model, and that Schwarz's model selection criterion BIC needs to be improved for Bayesian networks. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Bayesian Network / Stochastic Complesity / Algebraic Geometry |
| Paper # | NC2003-28 |
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| 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 | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Algebraic Geometry of Stochastic Complexity for Bayesian Networks |
| Sub Title (in English) | |
| Keyword(1) | Bayesian Network |
| Keyword(2) | Stochastic Complesity |
| Keyword(3) | Algebraic Geometry |
| 1st Author's Name | Keisuke YAMAZAKI |
| 1st Author's Affiliation | Tokyo Institute of Technology() |
| 2nd Author's Name | Sumio WATANABE |
| 2nd Author's Affiliation | Tokyo Institute of Technology |
| Date | 2003/7/21 |
| Paper # | NC2003-28 |
| Volume (vol) | vol.103 |
| Number (no) | 227 |
| Page | pp.pp.- |
| #Pages | 6 |
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