Approximation bound of mixture networks in Lwp spaces

Authors:
Zongben Xu;Jianjun Wang;Deyu Meng
Affiliations:
Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, P.R. China;Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, P.R. China;Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, P.R. China
Venue:
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Year:
2006

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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 $L^{p}_{\omega}$ Spaces and underlies applicability of the mixture neural networks.