| Presentation | 2012-11-08 On Dimensionality Recovery Guarantee of Variational Bayesian PCA Shinichi NAKAJIMA, Ryota TOMIOKA, Masashi SUGIYAMA, S. Derin BABACAN, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such sparsity is hardly observed in the rigorous Bayesian estimation. In this paper, we focus on probabilistic PCA and give more theoretical insight into the empirical success of VB. More specifically, for the situation where the noise variance is unknown, we derive a sufficient condition for perfect recovery of the true PCA dimensionality in the large-scale limit when the size of an observed matrix goes to infinity with its column-row ratio fixed. In our analysis, we obtain bounds for a noise variance estimator and simple closed-form solutions for other parameters, which themselves are actually very useful for better implementation of VB-PCA. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | matrix factorization / variational Bayes / sparsity / perfect dimensionality recovery |
| Paper # | IBISML2012-66 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2012/10/31(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| 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) | On Dimensionality Recovery Guarantee of Variational Bayesian PCA |
| Sub Title (in English) | |
| Keyword(1) | matrix factorization |
| Keyword(2) | variational Bayes |
| Keyword(3) | sparsity |
| Keyword(4) | perfect dimensionality recovery |
| 1st Author's Name | Shinichi NAKAJIMA |
| 1st Author's Affiliation | Optical Research Laboratory, Nikon Corporation() |
| 2nd Author's Name | Ryota TOMIOKA |
| 2nd Author's Affiliation | The University of Tokyo |
| 3rd Author's Name | Masashi SUGIYAMA |
| 3rd Author's Affiliation | Tokyo Institute of Technology |
| 4th Author's Name | S. Derin BABACAN |
| 4th Author's Affiliation | Beckman Institute, University of Illinois at Urbana-Champaign |
| Date | 2012-11-08 |
| Paper # | IBISML2012-66 |
| Volume (vol) | vol.112 |
| Number (no) | 279 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |