On the Degree of Approximation by Manifolds of Finite Pseudo-Dimension

@inproceedings{Maiorov1999OnTD,
  title={On the Degree of Approximation by Manifolds of Finite Pseudo-Dimension},
  author={Vitaly Maiorov and Joel Ratsaby},
  year={1999}
}
The pseudo-dimension of a real-valued function class is an extension of the VC dimension for set-indicator function classes. A class H of finite pseudo-dimension possesses a useful statistical smoothness property. In [10] we introduced a nonlinear approximation widthρn(F , Lq) = infHn dist(F ,Hn, Lq) which measures the worstcase approximation error over all functions f ∈ F by the best manifold of pseudodimensionn. In this paper we obtain tight upper and lower bounds on ρn(W r,d p , Lq), both… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 12 references

SOLOMJAK (1967):Piecewise-polynomial approximations of functions of the classes

M.Z.M.S. BIRMAN
W p . Math. USSR-Sb., • 1967
View 5 Excerpts
Highly Influenced

MAIOROV (1997):Generalization of the PAC-Model for learning with partial information

V. J. RATSABY
Proceedings of the Third European Conference on Computational Learning Theory, EuroCOLT • 1997
View 4 Excerpts
Highly Influenced

Constructive Approximation, Advanced Problems

G. G. LORENTZ, Y.M.V. GOLITSCHEK
MAKOVOZ • 1996

Empirical Processes: Theory and Applications

D. POLLARD
NSF-CAMS Regional Conference Series in Probability and Statistics, • 1989
View 3 Excerpts

Estimation of Dependences Based on

V N.
VAPNIK • 1982
View 1 Excerpt

Necessary and sufficient conditions for the uniform convergence of means to their expectations

V. N. VAPNIK, YA A.
CHERVONENKIS • 1981
View 1 Excerpt

Some Problems in Approximation Theory. Moscow: Moscow State University

V M.
TIKHOMIROV • 1976
View 1 Excerpt

CHERVONENKIS (1971):On the uniform convergence of relative frequencies of events to their probabilities

V. N. VAPNIK, YA A.
Theoret. Prob. Its Appl., • 1971
View 3 Excerpts

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