Radial basis function networks and complexity regularization in function learning

Authors:
A. Krzyzak;T. Linder
Affiliations:
Dept. of Comput. Sci., Concordia Univ., Montreal, Que.;-
Venue:
IEEE Transactions on Neural Networks
Year:
1998

Citing 0
Cited 12

Model Selection and Error Estimation

Machine Learning
Nonlinear Function Learning and Classification Using Optimal Radial Basis Function Networks

MLDM '01 Proceedings of the Second International Workshop on Machine Learning and Data Mining in Pattern Recognition
On-line RBFNN based identification of rapidly time-varying nonlinear systems with optimal structure-adaptation

Mathematics and Computers in Simulation
Density estimation by the penalized combinatorial method

Journal of Multivariate Analysis
Nonlinear Function Learning Using Radial Basis Function Networks: Convergence and Rates

ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Quasi-parametric recovery of Hammerstein system nonlinearity by smart model selection

ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
A review of wave-net identical learning & filling-in in a decomposition space of (JPG-JPEG) sampled images

Artificial Intelligence Review
Nonlinear function learning by the normalized radial basis function networks

ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
Approximation and estimation bounds for free knot splines

Computers & Mathematics with Applications
Incorporating linear discriminant analysis in neural tree for multidimensional splitting

Applied Soft Computing
Universal learning using free multivariate splines

Neurocomputing
Generalization ability of fractional polynomial models

Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

We apply the method of complexity regularization to derive estimation bounds for nonlinear function estimation using a single hidden layer radial basis function network. Our approach differs from previous complexity regularization neural-network function learning schemes in that we operate with random covering numbers and l1 metric entropy, making it possible to consider much broader families of activation functions, namely functions of bounded variation. Some constraints previously imposed on the network parameters are also eliminated this way. The network is trained by means of complexity regularization involving empirical risk minimization. Bounds on the expected risk in terms of the sample size are obtained for a large class of loss functions. Rates of convergence to the optimal loss are also derived