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Paper Abstract and Keywords
Presentation 2015-01-22 15:50
Covariance matrix estimation for multivariate Gaussian process regression
Yuki Matsumura, Toshikazu Wada (Wakayama Univ.) PRMU2014-98 MVE2014-60
Abstract (in Japanese) (See Japanese page) 
(in English) Gaussian process regression is a nonlinear regression that estimates the expected value of the of the output and its variance for given input. The original Gaussian process regression estimates a scalar value as an expected value of output, which can simply be extended to estimate a vector value. However, the covariance matrix cannot be estimated by simple extension. We have proposed an accelerated Gaussian process regression by introducing dynamic active set consisting of input-output pairs, and the weighted output covariance can be utilized as the covariance of output for multivariate Gaussian process regression. However, the diagonal elements of the estimated matrix can be negative. This is caused by the negative weight of the outputs originated by the inverse of gram matrix. In this report, we propose a method to estimate non-negative weights for the outputs. The estimation is twofold: initially estimate the output vector by simple multivariate Gaussian process regression, then re-compute non-negative weights so as to minimize the output error. The resulted weights are utilized to estimate covariance matrix. By using the proposed method in anomaly detection of plant data and electrocardiogram data in the experiment, it was confirmed its effectiveness.
Keyword (in Japanese) (See Japanese page) 
(in English) Gaussian Process Regression / Example based non-linear regression / covariance matrix estimation / / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 409, PRMU2014-98, pp. 117-122, Jan. 2015.
Paper # PRMU2014-98 
Date of Issue 2015-01-15 (PRMU, MVE) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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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 PRMU2014-98 MVE2014-60

Conference Information
Committee PRMU IPSJ-CVIM MVE  
Conference Date 2015-01-22 - 2015-01-23 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To PRMU 
Conference Code 2015-01-PRMU-CVIM-MVE 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Covariance matrix estimation for multivariate Gaussian process regression 
Sub Title (in English)  
Keyword(1) Gaussian Process Regression  
Keyword(2) Example based non-linear regression  
Keyword(3) covariance matrix estimation  
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1st Author's Name Yuki Matsumura  
1st Author's Affiliation Wakayama University (Wakayama Univ.)
2nd Author's Name Toshikazu Wada  
2nd Author's Affiliation Wakayama University (Wakayama Univ.)
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Speaker Author-1 
Date Time 2015-01-22 15:50:00 
Presentation Time 25 minutes 
Registration for PRMU 
Paper # PRMU2014-98, MVE2014-60 
Volume (vol) vol.114 
Number (no) no.409(PRMU), no.410(MVE) 
Page pp.117-122 
#Pages 6 
Date of Issue 2015-01-15 (PRMU, MVE) 

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