Generalization bounds for function approximation from scattered noisy data

@article{Niyogi1999GeneralizationBF,
  title={Generalization bounds for function approximation from scattered noisy data},
  author={Partha Niyogi and Federico Girosi},
  journal={Adv. Comput. Math.},
  year={1999},
  volume={10},
  pages={51-80}
}
We consider the problem of approximating functions from scattered data using linear superpositions of non-linearly parameterized functions. We show how the total error (generalization error) can be decomposed into two parts: an approximation part that is due to the finite number of parameters of the approximation scheme used; and an estimation part that is due to the finite number of data available. We bound each of these two parts under certain assumptions and prove a general bound for a class… CONTINUE READING
Highly Influential
This paper has highly influenced 10 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 41 extracted citations

Generalization Performance of Radial Basis Function Networks

IEEE Transactions on Neural Networks and Learning Systems • 2015
View 6 Excerpts
Highly Influenced

Generalization ability of fractional polynomial models

Neural Networks • 2014
View 6 Excerpts
Highly Influenced

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

Adv. Comput. Math. • 2000
View 6 Excerpts
Highly Influenced

Model Selection for Regularized Least-Squares Algorithm in Learning Theory

Foundations of Computational Mathematics • 2005
View 10 Excerpts
Highly Influenced

On Different Facets of Regularization Theory

Neural Computation • 2002
View 11 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-10 of 41 references

Universal approximation bounds for superpositions of a sigmoidal function

IEEE Trans. Information Theory • 1993
View 6 Excerpts
Highly Influenced

Degree of approximation by neural and translation networks with a single hidden layer

H. Mhaskar, C. Micchelli
Adv. Appl. Math • 1995
View 1 Excerpt

Rates of convergence for radial basis functions and neural networks, in: Artificial Neural Networks for Speech and Vision, ed

F. Girosi, G. Anzellotti
R.J. Mammone (Chapman and Hall, London, • 1993
View 2 Excerpts

Stacked regression, Technical Report

L. Breiman
1993
View 1 Excerpt

Similar Papers

Loading similar papers…