| Presentation | 2011-09-05 Global Solution of Variational Bayesian Matrix Factorization Under Matrix-wise Independence Shinichi NAKAJIMA, Masashi SUGIYAMA, Derin BABACAN, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Variational Bayesian matrix factorization (VBMF) efficiently approximates the posterior distribution of factorized matrices by assuming matrix-wise independence of the two factors. A recent study on fully-observed VBMF showed that, under a stronger assumption that the two factorized matrices are column-wise independent, the global optimal solution can be analytically computed. However, it was not clear how restrictive the column-wise independence assumption is. In this paper, we prove that the global solution under matrix-wise independence is actually column-wise independent, implying that the column-wise independence assumption is harmless. A practical consequence of our theoretical finding is that the global solution under matrix-wise independence (which is a standard setup) can be obtained analytically in a computationally very efficient way without any iterative algorithms. We experimentally illustrate advantages of using our analytic solution in probabilistic principal component analysis. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | matrix factorization / variational Bayes / matrix-wise independence / column-wise independence / probabilistic PCA |
| Paper # | PRMU2011-58,IBISML2011-17 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 2011/8/29(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Pattern Recognition and Media Understanding (PRMU) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Global Solution of Variational Bayesian Matrix Factorization Under Matrix-wise Independence |
| Sub Title (in English) | |
| Keyword(1) | matrix factorization |
| Keyword(2) | variational Bayes |
| Keyword(3) | matrix-wise independence |
| Keyword(4) | column-wise independence |
| Keyword(5) | probabilistic PCA |
| 1st Author's Name | Shinichi NAKAJIMA |
| 1st Author's Affiliation | Optical Research Laboratory, Nikon Corporation() |
| 2nd Author's Name | Masashi SUGIYAMA |
| 2nd Author's Affiliation | Tokyo Institute of Technology:JST PRESTO |
| 3rd Author's Name | Derin BABACAN |
| 3rd Author's Affiliation | Beckman Institute, University of Illinois at Urbana-Champaign |
| Date | 2011-09-05 |
| Paper # | PRMU2011-58,IBISML2011-17 |
| Volume (vol) | vol.111 |
| Number (no) | 193 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |