Function Estimation by Feedforward Sigmoidal Networks with Bounded Weights

Nageswara S.V. Rao; Vladimir Protopopescu

doi:10.1023/A:1009640613940

Function Estimation by Feedforward Sigmoidal Networks with Bounded Weights

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Abstract

We address the problem of estimating a function f : [0, 1]^d → [-L, L] by using feedforward sigmoidal networks with a single hidden layer and bounded weights. The only information about the function is provided by an identically independently distributed sample generated according to an unknown distribution. The quality of the estimate is quantified by the expected cost functional and depends on the sample size. We use Lipschitz properties of the cost functional and of the neural networks to derive the relationship between performance bounds and sample sizes within the framework of Valiant's probably approximately correct learning.

Original language	English
Pages (from-to)	125-131
Number of pages	7
Journal	Neural Processing Letters
Volume	7
Issue number	3
DOIs	https://doi.org/10.1023/A:1009640613940
State	Published - 1998

Funding

This research sponsored by the Engineering Research Program of the Office of Basic Energy Sciences, of the U.S. Department of Energy, under Contract No. DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp.

Keywords

Feedforward sigmoid networks
Function estimation
PAC learning

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abstract = "We address the problem of estimating a function f : [0, 1]d → [-L, L] by using feedforward sigmoidal networks with a single hidden layer and bounded weights. The only information about the function is provided by an identically independently distributed sample generated according to an unknown distribution. The quality of the estimate is quantified by the expected cost functional and depends on the sample size. We use Lipschitz properties of the cost functional and of the neural networks to derive the relationship between performance bounds and sample sizes within the framework of Valiant's probably approximately correct learning.",

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AU - Rao, Nageswara S.V.

AU - Protopopescu, Vladimir

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AB - We address the problem of estimating a function f : [0, 1]d → [-L, L] by using feedforward sigmoidal networks with a single hidden layer and bounded weights. The only information about the function is provided by an identically independently distributed sample generated according to an unknown distribution. The quality of the estimate is quantified by the expected cost functional and depends on the sample size. We use Lipschitz properties of the cost functional and of the neural networks to derive the relationship between performance bounds and sample sizes within the framework of Valiant's probably approximately correct learning.

KW - Feedforward sigmoid networks

KW - Function estimation

KW - PAC learning

UR - https://www.scopus.com/pages/publications/0032095771

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ER -

Function Estimation by Feedforward Sigmoidal Networks with Bounded Weights

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