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Paper Abstract and Keywords
Presentation 2009-01-19 11:45
A probabilistic model of maximum margin matrix factorization with ARD prior
Masahiro Furuya (Nara Inst. of Scie and Tech), Shigeyuki Oba (Kyoto Univ.), Shin Ishii (Nara Inst.of Scie and Tech/Kyoto Univ.) NC2008-85
Abstract (in Japanese) (See Japanese page) 
(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) 
(in English) Missing value prediction / Matrix factorization / Automatic relevance determination / Probabilistic model / / / /  
Reference Info. IEICE Tech. Rep., vol. 108, no. 383, NC2008-85, pp. 19-24, Jan. 2009.
Paper # NC2008-85 
Date of Issue 2009-01-12 (NC) 
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 NC2008-85

Conference Information
Committee NC  
Conference Date 2009-01-19 - 2009-01-20 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Neural Dynamics, etc. 
Paper Information
Registration To NC 
Conference Code 2009-01-NC 
Language Japanese 
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  
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1st Author's Name Masahiro Furuya  
1st Author's Affiliation Nara Institute of Science and Technology (Nara Inst. of Scie and Tech)
2nd Author's Name Shigeyuki Oba  
2nd Author's Affiliation Kyoto University (Kyoto Univ.)
3rd Author's Name Shin Ishii  
3rd Author's Affiliation Kyoto University (Nara Inst.of Scie and Tech/Kyoto Univ.)
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Speaker Author-1 
Date Time 2009-01-19 11:45:00 
Presentation Time 25 minutes 
Registration for NC 
Paper # NC2008-85 
Volume (vol) vol.108 
Number (no) no.383 
Page pp.19-24 
#Pages 6 
Date of Issue 2009-01-12 (NC) 

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