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Related Experiment Videos

Regularized neural networks: some convergence rate results

V Corradi1, H White

  • 1Department of Economics, University of Pennsylvania, Philadelphia, USA.

Neural Computation
|November 1, 1995
PubMed
Summary

Regularized neural networks can learn functions from noisy data, achieving optimal approximation rates in reproducing kernel Hilbert spaces (RKHS). If data doesn't fit RKHS, convergence is not guaranteed.

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Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Mathematical Analysis

Background:

  • Poggio and Girosi (1990) introduced regularized neural networks based on regularization theory.
  • These networks can approximate continuous functions on compact sets with arbitrary accuracy.

Purpose of the Study:

  • To analyze the learning problem for one-dimensional regularized networks.
  • To investigate the approximation capabilities with noisy output data.

Main Methods:

  • Analysis of regularized networks in the context of Sobolev and reproducing kernel Hilbert spaces (RKHS).
  • Derivation of error bounds based on the order of differentiability (m) of the unknown function.

Main Results:

  • For functions in RKHS, regularized networks achieve nonparametric learning rates of n^(-2m)/(2m+1).
  • If the function is not in an RKHS, a unique regularized solution exists but may not converge in mean square, or the error may be bounded away from zero.

Conclusions:

  • Regularized networks effectively learn from noisy data within RKHS, leveraging function smoothness for optimal convergence.
  • The theoretical framework highlights the importance of function space properties (RKHS) for guaranteed learning performance.

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