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Paper Abstract and Keywords
Presentation 2011-09-05 10:00
Global Solution of Variational Bayesian Matrix Factorization Under Matrix-wise Independence
Shinichi Nakajima (Nikon), Masashi Sugiyama (Tokyo Inst. of Tech.), Derin Babacan (Illinois Univ.) PRMU2011-58 IBISML2011-17
Abstract (in Japanese) (See Japanese page) 
(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) 
(in English) matrix factorization / variational Bayes / matrix-wise independence / column-wise independence / probabilistic PCA / / /  
Reference Info. IEICE Tech. Rep., vol. 111, no. 194, IBISML2011-17, pp. 1-8, Sept. 2011.
Paper # IBISML2011-17 
Date of Issue 2011-08-29 (PRMU, IBISML) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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)
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Conference Information
Conference Date 2011-09-05 - 2011-09-06 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IBISML 
Conference Code 2011-09-PRMU-IBISML-CVIM 
Language English (Japanese title is available) 
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 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 Derin Babacan  
3rd Author's Affiliation University of Illinois (Illinois Univ.)
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Speaker Author-1 
Date Time 2011-09-05 10:00:00 
Presentation Time 30 minutes 
Registration for IBISML 
Paper # PRMU2011-58, IBISML2011-17 
Volume (vol) vol.111 
Number (no) no.193(PRMU), no.194(IBISML) 
Page pp.1-8 
Date of Issue 2011-08-29 (PRMU, IBISML) 

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