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Local greedy approximation for nonlinear regression and neural network training. (English) Zbl 1105.62354
Summary: A criterion for local estimation and approximation in nonlinear regression and neural network training is introduced and motivated. \(N\) th-order greedy approximation for the regression (or target) function based on the criterion is shown to converge at rate \(O(1/N^{1/2})\) in the nonsampling case.

62J02 General nonlinear regression
62H12 Estimation in multivariate analysis
62M45 Neural nets and related approaches to inference from stochastic processes
Full Text: DOI
[1] Barron, A. R. (1993). Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 40 930-945. · Zbl 0818.68126
[2] Bottou, L. and Vapnik, V. (1992). Local learning algorithms. Neural Computation 4 888-900.
[3] Blum, A. L. and Rivest, R. L. (1992). Training a 3-Node Neural Network is NP-Complete. Neural Networks 5 117-127.
[4] DeVore, R. A. and Temlyakov, V. N. (1996). Some remarks on greedy algorithms. Adv. Comput. Math 5 173-187. · Zbl 0857.65016
[5] Donohue, M. J., Gurvitz, L., Darken, C. and Sontag, E. (1994). Rates of convex approximation in non-Hilbert spaces. Constr. Approx. 13 187-220. · Zbl 0876.41016
[6] Flick, T. E., Jones, L. K., Priest, R. and Herman, C.(1990). Projection pursuit classification. Pattern Recognition 23 1367-1376.
[7] Friedman, J. H. (1999). Greedy function approximation: a gradient boosting machine. Technical report, Stanford Univ. · Zbl 1043.62034
[8] Friedman, J. H. and Stuetzle, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76 817-823. JSTOR:
[9] Huber, P. J. (1985). Projection pursuit. Ann. Statist. 13 435-475. · Zbl 0595.62059
[10] Jones, L. K. (1987). On a conjuecture of Huber concerning the convergence of projection pursuit regression. Ann. Statist. 15 880-882. · Zbl 0664.62061
[11] Jones, L. K. (1992). A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Ann. Statist. 20 608-613. · Zbl 0746.62060
[12] Jones, L. K. (1994). Good weights and hyperbolic kernels for neural networks, projection pursuit, and pattern classification: Fourier strategies for extracting information from high-dimensional data. IEEE Trans. Inform. Theory 40 439-454. · Zbl 0941.68670
[13] Jones, L. K. (1997). The Computational intractability of training sigmoidal neural networks. IEEE Trans. Inform. Theory 43 167-173. · Zbl 0874.68255
[14] Lee, W. S. and Bartlett, P. L., and Williamson, R. C. (1996). Efficient agnostic learning of neural networks with bounded fan-in. IEEE Trans. Inform. Theory 42 2118-2132. · Zbl 0874.68253
[15] Rejto, L. and Walter, G. G. (1992). Remarks on projection pursuit regression and density estimation. Stochastic Anal. Appl. 10 213-222. · Zbl 0763.62034
[16] Vu, V. H. (1998). On the infeasibility of training neural networks with small mean-squared error. IEEE Trans. Inform. Theory 44 2892-2900. · Zbl 0981.68138
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