scholarly journals Representation of multivariate functions by sums of ridge functions

2007 ◽  
Vol 331 (1) ◽  
pp. 184-190 ◽  
Author(s):  
Vugar E. Ismailov
Keyword(s):  
Multivariate Functions ◽  
Ridge Functions

scholarly journals On sharpness of error bounds for multivariate neural network approximation

2020 ◽  
Author(s):  
Steffen Goebbels
Keyword(s):  
Error Bounds ◽  
Uniform Boundedness ◽  
Feedforward Neural Networks ◽  
Activation Function ◽  
Multivariate Functions ◽  
Non Linear ◽  
Uniform Boundedness Principle ◽  
Ridge Functions ◽  
Hidden Layer ◽  
Polynomial Activation Functions

AbstractSingle hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best non-linear approximation by such sums of ridge functions. Error bounds are presented in terms of moduli of smoothness. The main focus, however, is to prove that the bounds are best possible. To this end, counterexamples are constructed with a non-linear, quantitative extension of the uniform boundedness principle. They show sharpness with respect to Lipschitz classes for the logistic activation function and for certain piecewise polynomial activation functions. The paper is based on univariate results in Goebbels (Res Math 75(3):1–35, 2020. https://rdcu.be/b5mKH)

Fitting of multivariate functions

1987 ◽  
Vol 75 (7) ◽  
pp. 970-971 ◽  
Author(s):  
A.A. Georgiev
Keyword(s):  
Multivariate Functions

Automated establishment and plotting of multivariate functions

1990 ◽  
Vol 234 ◽  
pp. 493-497
Author(s):  
Zequn Yan ◽  
Xiaoheng Tang
Keyword(s):  
Multivariate Functions

scholarly journals Identifying Linear Combinations of Ridge Functions

1999 ◽  
Vol 22 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Martin D Buhmann ◽  
Allan Pinkus
Keyword(s):  
Linear Combinations ◽  
Ridge Functions

scholarly journals Decoupling multivariate functions using a non-parametric Filtered CPD approach

2021 ◽  
Vol 54 (7) ◽  
pp. 451-456
Author(s):  
Jan Decuyper ◽  
Koen Tiels ◽  
Siep Weiland ◽  
Johan Schoukens
Keyword(s):  
Multivariate Functions ◽  
Non Parametric
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