Nonparametric estimation and classification using radial basis function nets and empirical risk minimization
- 1 March 1996
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 7 (2) , 475-487
- https://doi.org/10.1109/72.485681
Abstract
Studies convergence properties of radial basis function (RBF) networks for a large class of basis functions, and reviews the methods and results related to this topic. The authors obtain the network parameters through empirical risk minimization. The authors show the optimal nets to be consistent in the problem of nonlinear function approximation and in nonparametric classification. For the classification problem the authors consider two approaches: the selection of the RBF classifier via nonlinear function estimation and the direct method of minimizing the empirical error probability. The tools used in the analysis include distribution-free nonasymptotic probability inequalities and covering numbers for classes of functions.Keywords
This publication has 30 references indexed in Scilit:
- On radial basis function nets and kernel regression: Statistical consistency, convergence rates, and receptive field sizeNeural Networks, 1994
- Rival penalized competitive learning for clustering analysis, RBF net, and curve detectionIEEE Transactions on Neural Networks, 1993
- A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network TrainingThe Annals of Statistics, 1992
- Universal Approximation Using Radial-Basis-Function NetworksNeural Computation, 1991
- Layered Neural Networks with Gaussian Hidden Units as Universal ApproximationsNeural Computation, 1990
- Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappingsNeural Networks, 1990
- An equivalence theorem for L1 convergence of the kernel regression estimateJournal of Statistical Planning and Inference, 1989
- Fast Learning in Networks of Locally-Tuned Processing UnitsNeural Computation, 1989
- What Size Net Gives Valid Generalization?Neural Computation, 1989
- Automatic pattern recognition: a study of the probability of errorPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1988