Approximation by sums of ridge functions with fixed directions
From MaRDI portal
Publication:5369335
DOI10.1090/spmj/1471zbMath1372.41009OpenAlexW2763388430MaRDI QIDQ5369335
Publication date: 17 October 2017
Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/spmj/1471
Related Items
Modeling regular textures in images using the Radon transform ⋮ On the approximation by single hidden layer feedforward neural networks with fixed weights ⋮ Gaussian functions combined with Kolmogorov's theorem as applied to approximation of functions of several variables ⋮ Approximation Properties of Ridge Functions and Extreme Learning Machines ⋮ A note on continuous sums of ridge functions ⋮ On the representation by bivariate ridge functions ⋮ A representation problem for smooth sums of ridge functions ⋮ ON THE ERROR OF APPROXIMATION BY RBF NEURAL NETWORKS WITH TWO HIDDEN NODES
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The ridge function representation of polynomials and an application to neural networks
- Approximation by neural networks with weights varying on a finite set of directions
- A note on the representation of continuous functions by linear superpositions
- Approximation by a sum of two algebras. The lightning bolt principle
- On the theorem of M. Golomb
- Projection-based approximation and a duality with kernel methods
- Approximation theory in tensor product spaces
- Dimension, superposition of functions and separation of points, in compact metric spaces
- Projection pursuit
- Uniform separation of points and measures and representation by sums of algebras
- Interpolation by piecewise-linear radial basis functions. I
- On the approximation of a bivariate function by the sum of univariate functions
- Approximation by Ridge functions and neural networks with one hidden layer
- Optimal reconstruction of a function from its projections
- Uniformly separating families of functions
- Identifying linear combinations of ridge functions
- On best approximation by ridge functions
- When is \(f(x,y)=u(x)+v(y)\)?
- Lower bounds for approximation by MLP neural networks
- Fundamentality of ridge functions
- Approximation by neural networks with a bounded number of nodes at each level
- When is \(f(x_1,x_1,\dots,x_n)= u_1(x_1)+ u_2(x_2)+\cdots+ u_n(x_n)\)?
- Ridgelets: estimating with ridge functions
- Training multilayer perceptrons via minimization of sum of ridge functions
- Interpolation by ridge polynomials and its application in neural networks
- Interpolation by Ridge functions
- On the reconstruction of a function on a circular domain from a sampling of its line integrals
- On existence of a best uniform approximation of a function in two variables by the sums \(\varphi (x)+ \psi (y)\)
- Nonlinearity creates linear independence
- Characterization of an extremal sum of ridge functions
- On the representation by linear superpositions
- On error formulas for approximation by sums of univariate functions
- Approximation by neural networks and learning theory
- On approximation theory and functional equations
- An improvement in the superposition theorem of Kolmogorov
- On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables
- Théorie générale des fonctions moyenne-périodiques
- On the approximation of a function of several variables by the sum of functions of fewer variables
- Universal Approximation by Ridge Computational Models and Neural Networks: A Survey
- Sums of Subalgebras of C (X )
- On Nonlinear Functions of Linear Combinations
- Uniform approximation by real functions
- Approximation by Solutions of the Planar Wave Equation
- A Superposition Theorem for Bounded Continuous Functions
- Tomographic reconstruction from arbitrary directions using ridge functions
- Approximation by Ridge Functions and Neural Networks
- A Projection Pursuit Algorithm for Exploratory Data Analysis
- Reconstruction of elongated structures using ridge functions and natural pixels
- Metric Entropy, Widths, and Superpositions of Functions
- Dimension of metric spaces and Hilbert’s problem 13
- Approximation by superpositions of a sigmoidal function