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 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. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | Multi-layer perceptron / Fisher information matrix / Positive difiniteness / Irreducibility / Minimality / Complex analysis |
Paper # | NC94-33 |
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Committee | NC |
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Conference Date | 1994/10/13(1days) |
Place (in Japanese) | (See Japanese page) |
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Registration To | Neurocomputing (NC) |
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Language | JPN |
Title (in Japanese) | (See Japanese page) |
Sub Title (in Japanese) | (See Japanese page) |
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 |
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