| Presentation | 2020-01-09 Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures Takumi Watanabe, Sumio Watanabe, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Multinomial mixtures are widely used in the information engineering field. However, it is not subject to the conventional statistical theory of regular statistical models, because the models are not identifiable and their Fisher information matrices are is not positive definite. In the recent years, the generalization performance of singular learning machines was clarified based on resolution of singularities. In this report, we compute Real Log Canonical Thresholds in an algebraic geometric way and clarify asymptotic behaviors of generalization error and free energy. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | generalization error / free energy / multinomial mixtures / real log canonical thresholds |
| Paper # | IBISML2019-18 |
| Date of Issue | 2020-01-02 (IBISML) |
| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2020/1/9(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | ISM |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Machine learning, etc. |
| Chair | Hisashi Kashima(Kyoto Univ.) |
| Vice Chair | Masashi Sugiyama(Univ. of Tokyo) / Koji Tsuda(Univ. of Tokyo) |
| Secretary | Masashi Sugiyama(Nagoya Inst. of Tech.) / Koji Tsuda(AIST) |
| Assistant | Tomoharu Iwata(NTT) / Shigeyuki Oba(Kyoto Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures |
| Sub Title (in English) | |
| Keyword(1) | generalization error |
| Keyword(2) | free energy |
| Keyword(3) | multinomial mixtures |
| Keyword(4) | real log canonical thresholds |
| 1st Author's Name | Takumi Watanabe |
| 1st Author's Affiliation | Tokyo Institute of Technology(Tokyo Tech) |
| 2nd Author's Name | Sumio Watanabe |
| 2nd Author's Affiliation | Tokyo Institute of Technology(Tokyo Tech) |
| Date | 2020-01-09 |
| Paper # | IBISML2019-18 |
| Volume (vol) | vol.119 |
| Number (no) | IBISML-360 |
| Page | pp.pp.1-8(IBISML), |
| #Pages | 8 |
| Date of Issue | 2020-01-02 (IBISML) |