A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training

A general convergence criterion for certain iterative sequences in Hilbert space is presented. For an important subclass of these sequences, estimates of the rate of convergence are given. Under very mild assumptions these results establish an$O(1/ \sqrt n)$nonsampling convergence rate for projectio...

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Veröffentlicht in:	The Annals of statistics 1992-03, Vol.20 (1), p.608-613
1. Verfasser:	Jones, Lee K.
Format:	Artikel
Sprache:	eng
Schlagworte:	62H99 Approximation Artificial neural networks Exact sciences and technology greedy expansion Hilbert spaces Mathematical foundations Mathematical functions Mathematics neural network Perceptron convergence procedure Probability and statistics Projection pursuit Sciences and techniques of general use Short Communications Statistics
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description	A general convergence criterion for certain iterative sequences in Hilbert space is presented. For an important subclass of these sequences, estimates of the rate of convergence are given. Under very mild assumptions these results establish an$O(1/ \sqrt n)$nonsampling convergence rate for projection pursuit regression and neural network training; where n represents the number of ridge functions, neurons or coefficients in a greedy basis expansion.
doi_str_mv	10.1214/aos/1176348546
format	Article
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source	JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete
subjects	62H99 Approximation Artificial neural networks Exact sciences and technology greedy expansion Hilbert spaces Mathematical foundations Mathematical functions Mathematics neural network Perceptron convergence procedure Probability and statistics Projection pursuit Sciences and techniques of general use Short Communications Statistics
title	A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training
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