| Presentation | 2017-09-15 Experimental Analysis of Variational Bayesian Method in Model Selection of Gaussian Mixture Model by Singular Bayesian Information Criterion Naoki Hayashi, Fumito Nakamura, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | A Gaussian mixture model (GMM) is a statistical model used in various fields such a pattern recognition, thus, it is important to resolve its model selection problems, however, GMM is not statistical regular since the map from the set of parameters to the set of probability density functions is not injective. Recently, a statistical model selection criterion, called the singular Bayesian information criterion (sBIC) has been proposed and it can be applied even if the statistical model is not regular. The model selection of GMM is carried out using by the local maximum likelihood estimator (LMLE) calculated by the EM algorithm for sBIC. On the other hand, the variational Bayesian method is also applied to estimate GMM because of that there does not exists the maximum likelihood estimator. In this paper, we consider the numerical behavior of the model selection of GMMs using by sBIC that is evaluated the estimator by the variational Bayesian method (variational Bayesian estimator, VBE) instead of LMLE. We compare with the cases that sBIC uses the LMLE, and report that sBIC that uses the VBE estimates more rigorous in both the case (1) that only the components' means and the mixtured ratio are estimated and the case (2) that the covariance is additionally did. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Gaussian mixture model / model selection / EM algorithm / variational Bayesian method / real log canonical threshold / singular Bayesian information criterion / sBIC |
| Paper # | PRMU2017-41,IBISML2017-13 |
| Date of Issue | 2017-09-08 (PRMU, IBISML) |
| Conference Information | |
| Committee | PRMU / IBISML / IPSJ-CVIM |
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| Conference Date | 2017/9/15(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Shinichi Sato(NII) / Kenji Fukumizu(ISM) |
| Vice Chair | Hironobu Fujiyoshi(Chubu Univ.) / Yoshihisa Ijiri(Omron) / Masashi Sugiyama(Univ. of Tokyo) |
| Secretary | Hironobu Fujiyoshi(AIST) / Yoshihisa Ijiri(NAIST) / Masashi Sugiyama(Kyoto Univ.) / (Univ. of Tokyo) |
| Assistant | Masato Ishii(NEC) / Yusuke Sugano(Osaka Univ.) / Ichiro Takeuchi(Nagoya Inst. of Tech.) / Toshihiro Kamishima(AIST) |
| Paper Information | |
| Registration To | Technical Committee on Pattern Recognition and Media Understanding / Technical Committee on Infomation-Based Induction Sciences and Machine Learning / Special Interest Group on Computer Vision and Image Media |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Experimental Analysis of Variational Bayesian Method in Model Selection of Gaussian Mixture Model by Singular Bayesian Information Criterion |
| Sub Title (in English) | |
| Keyword(1) | Gaussian mixture model |
| Keyword(2) | model selection |
| Keyword(3) | EM algorithm |
| Keyword(4) | variational Bayesian method |
| Keyword(5) | real log canonical threshold |
| Keyword(6) | singular Bayesian information criterion |
| Keyword(7) | sBIC |
| 1st Author's Name | Naoki Hayashi |
| 1st Author's Affiliation | Tokyo Institute of Technology(Tokyo Tech) |
| 2nd Author's Name | Fumito Nakamura |
| 2nd Author's Affiliation | Bosch Corporation(Bosch) |
| Date | 2017-09-15 |
| Paper # | PRMU2017-41,IBISML2017-13 |
| Volume (vol) | vol.117 |
| Number (no) | PRMU-210,IBISML-211 |
| Page | pp.pp.19-26(PRMU), pp.19-26(IBISML), |
| #Pages | 8 |
| Date of Issue | 2017-09-08 (PRMU, IBISML) |