| Presentation | 2009-01-19 A probabilistic model of maximum margin matrix factorization with ARD prior Masahiro FURUYA, Shigeyuki OBA, Shin ISHII, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Various methods for missing value estimation of matrix data have been proposed based on low-rank approximation of matrix data. A recent example is the maximum margin matrix factorization(MMMF) (Srebro and Rennie, 2005) proposed for predicting discrete values such as binary and ordinal rating. The MMMF is characterized with a penalty term based on a hinge error function and a regularization term based on a trace norm. An important key in matrix factorization is to determine hyper-parameters, such as approximated rank and regularization factor, which affect much to generalization performances. But, when there are multiple hyper-parameters to be determined, grid search with cross-validation takes large computational cost. In this report, we consider a probabilistic approach to determine the hyper-parameters based on the evidence criterion and propose a probabilistic MMMF(PMMMF) model that includes a prior of factor matrix with automatic relevance determination(ARD) hyper-parameter. This approach enables us to automatically determine both the regularization factor and rank that improve the generalization performance. We compare the proposed and original methods and show a better result on a real collaborative filtering problem. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Missing value prediction / Matrix factorization / Automatic relevance determination / Probabilistic model |
| Paper # | NC2008-85 |
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| Committee | NC |
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| Conference Date | 2009/1/12(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Neurocomputing (NC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A probabilistic model of maximum margin matrix factorization with ARD prior |
| Sub Title (in English) | |
| Keyword(1) | Missing value prediction |
| Keyword(2) | Matrix factorization |
| Keyword(3) | Automatic relevance determination |
| Keyword(4) | Probabilistic model |
| 1st Author's Name | Masahiro FURUYA |
| 1st Author's Affiliation | Graduate School of Information Science, Nara Institute of Science and Technology() |
| 2nd Author's Name | Shigeyuki OBA |
| 2nd Author's Affiliation | Graduate School of Informatics, Kyoto University |
| 3rd Author's Name | Shin ISHII |
| 3rd Author's Affiliation | Graduate School of Informatics, Kyoto University:Graduate School of Information Science, Nara Institute of Science and Technology |
| Date | 2009-01-19 |
| Paper # | NC2008-85 |
| Volume (vol) | vol.108 |
| Number (no) | 383 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |