Training neural networks with noisy data as an ill-posed problem

被引：0

作者：

Martin Burger

Heinz W. Engl

机构：

[1] Johannes Kepler Universität Linz,Industrial Mathematics Institute

来源：

Advances in Computational Mathematics | 2000年 / 13卷

关键词：

ill-posed problems; least-squares collocation; neural networks; network training; regularization;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper is devoted to the analysis of network approximation in the framework of approximation and regularization theory. It is shown that training neural networks and similar network approximation techniques are equivalent to least-squares collocation for a corresponding integral equation with mollified data.

引用

页码：335 / 354

页数：19

共 50 条

[1] Training neural networks with noisy data as an ill-posed problem
Burger, M
Engl, HW
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2000, 13 (04) : 335 - 354
[2] Learning in evolutive neural architectures: An ill-posed problem?
Jutten, C
FROM NATURAL TO ARTIFICIAL NEURAL COMPUTATION, 1995, 930 : 361 - 373
[3] SOLVING ILL-POSED PROBLEMS WITH ARTIFICIAL NEURAL NETWORKS
KULKARNI, AD
NEURAL NETWORKS, 1991, 4 (04) : 477 - 484
[4] UNIQUENESS FOR AN ILL-POSED PROBLEM
LERNER, N
JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 71 (02) : 255 - 260
[5] On a monotone ill-posed problem
Buong, N
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (05) : 1001 - 1004
[6] AN ILL-POSED DIFFRACTION PROBLEM
KARNOVSKII, MI
LOZOVIK, VG
OBOZNENKO, IL
SOVIET PHYSICS ACOUSTICS-USSR, 1979, 25 (06): : 497 - 500
[7] ON THE APPROXIMATION OF AN ILL-POSED PROBLEM
TIBA, D
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (05): : 619 - 624
[8] Detection of hormesis by empirical data as an ill-posed problem
Markovich, NM
AUTOMATION AND REMOTE CONTROL, 2000, 61 (01) : 125 - 135
[9] The Ill-Posed Problem in DIC
Lehoucq, Rich
Turner, Dan
INTERNATIONAL DIGITAL IMAGING CORRELATION SOCIETY, 2017, : 21 - 23
[10] Superparamagnetic clustering of data - The definitive solution of an ill-posed problem
Domany, E
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1999, 263 (1-4) : 158 - 169

← 1 2 3 4 5 →