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Paper Abstract and Keywords
Presentation 2017-03-06 14:30
Degrees of freedom in submodular regularization
Kentaro Minami, Fumiyasu Komaki (The University of Tokyo) IBISML2016-102
Abstract (in Japanese) (See Japanese page) 
(in English) We study two classes of convex regularization related to submodular functions, which we call the submodular regularization. In recent years, it has been pointed out by several authors that the submodular regularization can comprehensively handle a wide class of structural regularization in regression problems. From a computational perspective, estimators can be calculated by solving tractable convex minimization problems, in which the proximal gradient algorithms can be efficiently executed through submodular function minimization. However, from a statistical perspective, theoretical analysis of the mean squared error has not been investigated as an applicable form to general submodular regularizers. In this paper, we derive the degrees of freedom for submodular regularization estimators. The unbiased estimator of the degrees of freedom is given by the number of distinct values in the solution, which is consistent with existing results for the lasso and the fused lasso.
Keyword (in Japanese) (See Japanese page) 
(in English) sparse estimation / fused regularization / submodular function / model selection / / / /  
Reference Info. IEICE Tech. Rep., vol. 116, no. 500, IBISML2016-102, pp. 17-24, March 2017.
Paper # IBISML2016-102 
Date of Issue 2017-02-27 (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
Committee IBISML  
Conference Date 2017-03-06 - 2017-03-07 
Place (in Japanese) (See Japanese page) 
Place (in English) Tokyo Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Statistical Mathematics, Machine Learning, Data Mining, etc. 
Paper Information
Registration To IBISML 
Conference Code 2017-03-IBISML 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Degrees of freedom in submodular regularization 
Sub Title (in English)  
Keyword(1) sparse estimation  
Keyword(2) fused regularization  
Keyword(3) submodular function  
Keyword(4) model selection  
1st Author's Name Kentaro Minami  
1st Author's Affiliation The University of Tokyo (The University of Tokyo)
2nd Author's Name Fumiyasu Komaki  
2nd Author's Affiliation The University of Tokyo (The University of Tokyo)
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Speaker Author-1 
Date Time 2017-03-06 14:30:00 
Presentation Time 30 minutes 
Registration for IBISML 
Paper # IBISML2016-102 
Volume (vol) vol.116 
Number (no) no.500 
Page pp.17-24 
Date of Issue 2017-02-27 (IBISML) 

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