Approximation bound of mixture networks in Lω pspaces

Zongben Xu; Jianjun Wang; Deyu Meng

doi:10.1007/11759966_9

Approximation bound of mixture networks in L_ω ^pspaces

Zongben Xu
, Jianjun Wang
, Deyu Meng

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The approximation order estimation problem for multidimensional functions by the mixture of experts neural networks is studied. It is shown that under very mild condition on activation functions, the mixture neural networks have the same approximation order with that of the normal feedforward sigmoid neural networks. The obtained result sharpens the estimation developed by Maiorov and Meir in IEEE Trans. on Neural Networks (9(1998),969-978) over the compact region in L_ω^p Spaces and underlies applicability of the mixture neural networks.

Original language	English
Title of host publication	Advances in Neural Networks - ISNN 2006
Subtitle of host publication	Third International Symposium on Neural Networks, ISNN 2006, Proceedings
Publisher	Springer Verlag
Pages	60-65
Number of pages	6
ISBN (Print)	354034439X, 9783540344391
DOIs	https://doi.org/10.1007/11759966_9
State	Published - 2006
Event	3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks - Chengdu, China Duration: 28 May 2006 → 1 Jun 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3971 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks
Country/Territory	China
City	Chengdu
Period	28/05/06 → 1/06/06

Access to Document

10.1007/11759966_9

Cite this

Xu, Z., Wang, J., & Meng, D. (2006). Approximation bound of mixture networks in L_ω ^pspaces. In Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings (pp. 60-65). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3971 LNCS). Springer Verlag. https://doi.org/10.1007/11759966_9

Xu, Zongben ; Wang, Jianjun ; Meng, Deyu. / Approximation bound of mixture networks in L_ω ^pspaces. Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag, 2006. pp. 60-65 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Approximation bound of mixture networks in Lω pspaces",

abstract = "The approximation order estimation problem for multidimensional functions by the mixture of experts neural networks is studied. It is shown that under very mild condition on activation functions, the mixture neural networks have the same approximation order with that of the normal feedforward sigmoid neural networks. The obtained result sharpens the estimation developed by Maiorov and Meir in IEEE Trans. on Neural Networks (9(1998),969-978) over the compact region in Lωp Spaces and underlies applicability of the mixture neural networks.",

author = "Zongben Xu and Jianjun Wang and Deyu Meng",

year = "2006",

doi = "10.1007/11759966\_9",

language = "英语",

isbn = "354034439X",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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booktitle = "Advances in Neural Networks - ISNN 2006",

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Xu, Z, Wang, J & Meng, D 2006, Approximation bound of mixture networks in L_ω ^pspaces. in Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3971 LNCS, Springer Verlag, pp. 60-65, 3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks, Chengdu, China, 28/05/06. https://doi.org/10.1007/11759966_9

Approximation bound of mixture networks in L_ω ^pspaces. / Xu, Zongben; Wang, Jianjun; Meng, Deyu.
Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag, 2006. p. 60-65 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3971 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The approximation order estimation problem for multidimensional functions by the mixture of experts neural networks is studied. It is shown that under very mild condition on activation functions, the mixture neural networks have the same approximation order with that of the normal feedforward sigmoid neural networks. The obtained result sharpens the estimation developed by Maiorov and Meir in IEEE Trans. on Neural Networks (9(1998),969-978) over the compact region in Lωp Spaces and underlies applicability of the mixture neural networks.

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Xu Z, Wang J, Meng D. Approximation bound of mixture networks in L_ω ^pspaces. In Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag. 2006. p. 60-65. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11759966_9