Accuracy analysis for wavelet approximations
- 1 March 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 6 (2), 332-348
- https://doi.org/10.1109/72.363469
Abstract
"Constructive wavelet networks" are investigated as a universal tool for function approximation. The parameters of such networks are obtained via some "direct" Monte Carlo procedures. Approximation bounds are given. Typically, it is shown that such networks with one layer of "wavelons" achieve an L/sub 2/ error of order O(N/sup -(/spl rhod)/), where N is the number of nodes, d is the problem dimension and /spl rho/ is the number of summable derivatives of the approximated function. An algorithm is also proposed to estimate this approximation based on noisy input-output data observed from the function under consideration. Unlike neural network training, this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated "backpropagation" and it completely avoids the problem of poor convergence or undesirable local minima.<>Keywords
This publication has 12 references indexed in Scilit:
- Ten Lectures on WaveletsThe Journal of the Acoustical Society of America, 1993
- Minimax Theory of Image ReconstructionPublished by Springer Science and Business Media LLC ,1993
- Density estimation in Besov spacesStatistics & Probability Letters, 1992
- Applied Nonparametric RegressionPublished by Cambridge University Press (CUP) ,1990
- Networks for approximation and learningProceedings of the IEEE, 1990
- Approximation by superpositions of a sigmoidal functionMathematics of Control, Signals, and Systems, 1989
- Universal approximation using feedforward networks with non-sigmoid hidden layer activation functionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Construction of neural nets using the radon transformPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Optimal Global Rates of Convergence for Nonparametric RegressionThe Annals of Statistics, 1982
- Interpolation SpacesGrundlehren der mathematischen Wissenschaften, 1976