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| Presentation | 2010-11-05 15:30 [Poster Presentation] Global Analytic Solution for Variational Bayesian Matrix Factorization and its Model-induced Regularization Shinichi Nakajima (Nikon), Masashi Sugiyama (Tokyo Inst. of Tech.), Ryota Tomioka (Univ. of Tokyo)  IBISML2010-99 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we first show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic equation. This is highly advantageous over a popular VBMF algorithm based on iterated conditional modes since it can only find a local optimal solution after iterations. We further show that the global optimal solution of empirical VBMF (hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments. Our analysis reveals details of an unintentional regularization effect, which we call model-induced regularization (MIR). Showing its relation to shrinkage estimators, we discuss MIR in detail. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | variational Bayes / matrix factorization / non-identifiable models / model-induced regularization / James-Stein shrinkage / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 110, no. 265, IBISML2010-99, pp. 291-302, Nov. 2010. | |
| Paper # | IBISML2010-99 | |
| Date of Issue | 2010-10-28 (IBISML) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | IBISML2010-99 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2010-11-04 - 2010-11-06 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | IIS, Univ. of Tokyo |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | IBIS 2010 (Workshop on Information-based Induction Sciences) |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2010-11-IBISML |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Global Analytic Solution for Variational Bayesian Matrix Factorization and its Model-induced Regularization |
| Sub Title (in English) | |
| Keyword(1) | variational Bayes |
| Keyword(2) | matrix factorization |
| Keyword(3) | non-identifiable models |
| Keyword(4) | model-induced regularization |
| Keyword(5) | James-Stein shrinkage |
| Keyword(6) | |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Shinichi Nakajima |
| 1st Author's Affiliation | Nikon Corporation (Nikon) |
| 2nd Author's Name | Masashi Sugiyama |
| 2nd Author's Affiliation | Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
| 3rd Author's Name | Ryota Tomioka |
| 3rd Author's Affiliation | The University of Tokyo (Univ. of Tokyo) |
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| Speaker | Author-1 |
| Date Time | 2010-11-05 15:30:00 |
| Presentation Time | 180 minutes |
| Registration for | IBISML |
| Paper # | IBISML2010-99 |
| Volume (vol) | vol.110 |
| Number (no) | no.265 |
| Page | pp.291-302 |
| #Pages | 12 |
| Date of Issue | 2010-10-28 (IBISML) |
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