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Paper Abstract and Keywords
Presentation 2007-03-14 09:50
Estimation of poles of zeta function in learning theory using pade approximation
Ryosuke Iriguchi, Sumio Watanabe (Tokyo Tech.)
Abstract (in Japanese) (See Japanese page) 
(in English) Learning machines such as neural networks, Gaussian mixtures, Bayes networks, hidden Markov models, and Boltzmann machines are called singular learning machines, which have been applied to many real problems such as pattern recognition, time-series prediction, and system control. However, these learning machines have singular points which are attributable to their hierarchical structures or symmetry property. Hence, the maximum likelihood estimators do not have asymptotic normality, and conventional asymptotic theory for statistical regular models can not be applied. Therefore, theoretical optimal model selections or designs involve algebraic geometrical analysis. The algebraic geometrical analysis requires blowing up, which is to obtain maximum poles of zeta functions in learning theory, however, it is hard for complex learning machines. In this paper, a new method which obtains the maximum poles of zeta functions in learning theory by numerical computations is proposed.
Keyword (in Japanese) (See Japanese page) 
(in English) Singular Learning Machine / Beyes Learning / Learning Coefficient / Zeta Function / Pade Approximation / / /  
Reference Info. IEICE Tech. Rep., vol. 106, no. 588, NC2006-135, pp. 103-108, March 2007.
Paper # NC2006-135 
Date of Issue 2007-03-07 (NC) 
ISSN Print edition: ISSN 0913-5685
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Conference Information
Committee NC  
Conference Date 2007-03-14 - 2007-03-16 
Place (in Japanese) (See Japanese page) 
Place (in English) Tamagawa University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) General 
Paper Information
Registration To NC 
Conference Code 2007-03-NC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Estimation of poles of zeta function in learning theory using pade approximation 
Sub Title (in English)  
Keyword(1) Singular Learning Machine  
Keyword(2) Beyes Learning  
Keyword(3) Learning Coefficient  
Keyword(4) Zeta Function  
Keyword(5) Pade Approximation  
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1st Author's Name Ryosuke Iriguchi  
1st Author's Affiliation Tokyo Institute of Technology (Tokyo Tech.)
2nd Author's Name Sumio Watanabe  
2nd Author's Affiliation Tokyo Institute of Technology (Tokyo Tech.)
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Speaker Author-1 
Date Time 2007-03-14 09:50:00 
Presentation Time 20 minutes 
Registration for NC 
Paper # NC2006-135 
Volume (vol) vol.106 
Number (no) no.588 
Page pp.103-108 
#Pages
Date of Issue 2007-03-07 (NC) 


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