Presentation 1994/10/13
An irreducible multi-layer perceptron has a positive definite Fisher information matrix
Kenji Fukumizu, Sumio Watanabe,
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Abstract(in Japanese) (See Japanese page)
Abstract(in English) It is known that the Fisher information matrix of a multi-layer perceptron can be singular at certain parameters.In such a case many statistical techniques based on asymptotic theory fail to be applied properly.In this paper we prove rigorously that the Fisher information matrix of a three-layer perceptron is positive definite if and only if the network is irreducible,i.e.if,there do not exist a hidden unit that makes no contribution to the output, and there is no pair of hidden units that could be collapsed to a single unit without altering the input-output map.This fact implies,that,if a network has a singulax Fisher information matrix, it can be reduced to a network with a positive definite Fisher Information matrix by eliminating redundant hidden units.
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Keyword(in English) Multi-layer perceptron / Fisher information matrix / Positive difiniteness / Irreducibility / Minimality / Complex analysis
Paper # NC94-33
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Committee NC
Conference Date 1994/10/13(1days)
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Registration To Neurocomputing (NC)
Language JPN
Title (in Japanese) (See Japanese page)
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Title (in English) An irreducible multi-layer perceptron has a positive definite Fisher information matrix
Sub Title (in English)
Keyword(1) Multi-layer perceptron
Keyword(2) Fisher information matrix
Keyword(3) Positive difiniteness
Keyword(4) Irreducibility
Keyword(5) Minimality
Keyword(6) Complex analysis
1st Author's Name Kenji Fukumizu
1st Author's Affiliation Ricoh()
2nd Author's Name Sumio Watanabe
2nd Author's Affiliation Ricoh
Date 1994/10/13
Paper # NC94-33
Volume (vol) vol.94
Number (no) 272
Page pp.pp.-
#Pages 8
Date of Issue