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 |
Download PDF |
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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) |
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Keyword(1) |
Singular Learning Machine |
Keyword(2) |
Beyes Learning |
Keyword(3) |
Learning Coefficient |
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Zeta Function |
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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 |
6 |
Date of Issue |
2007-03-07 (NC) |
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