| Presentation | 2014-11-17 Theoretical Analysis of Empirical MAP and Empirical Partially Bayes Shinichi NAKAJIMA, Masashi SUGIYAMA, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Variational Bayesian (VB) learning is known to be a promising approximation to Bayesian learning with computational efficiency. However, in some applications, e.g., large-scale collaborative filtering and tensor factorization, VB is still computationally too costly. In such cases, looser approximations such as MAP estimation and partially Bayesian (PB) learning, where a part of the parameters are point-estimated, seem attractive. In this paper, we theoretically investigate the behavior of the MAP and the PB solutions of matrix factorization. A notable finding is that the global solutions of MAP and PB in the empirical Bayesian scenario, where the hyperparameters are also estimated from observation, are trivial and useless, while their local solutions behave similarly to the global solution of VB. This suggests that empirical MAP and empirical PB with local search can be alternatives to empirical VB equipped with the useful automatic relevance determination property. Experiments support our theory. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Empirical Bayes / partially Bayes / variational Bayes / global solution / local solution |
| Paper # | IBISML2014-38 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2014/11/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Information-Based Induction Sciences and Machine Learning (IBISML) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Theoretical Analysis of Empirical MAP and Empirical Partially Bayes |
| Sub Title (in English) | |
| Keyword(1) | Empirical Bayes |
| Keyword(2) | partially Bayes |
| Keyword(3) | variational Bayes |
| Keyword(4) | global solution |
| Keyword(5) | local solution |
| 1st Author's Name | Shinichi NAKAJIMA |
| 1st Author's Affiliation | Berlin Big Data Center, Technische Universitat Berlin() |
| 2nd Author's Name | Masashi SUGIYAMA |
| 2nd Author's Affiliation | University of Tokyo |
| Date | 2014-11-17 |
| Paper # | IBISML2014-38 |
| Volume (vol) | vol.114 |
| Number (no) | 306 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |