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Related Experiment Videos

Model complexity control for regression using VC generalization bounds.

V Cherkassky1, X Shao, F M Mulier

  • 1Electrical and Computer Engineering Department, University of Minnesota, Minneapolis MN 55455, USA.

IEEE Transactions on Neural Networks
|February 7, 2008
PubMed
Summary
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Complexity control is crucial for machine learning models. This study shows Vapnik-Chervonenkis (VC)-bounds offer superior complexity control in regression problems with finite samples compared to traditional methods.

Area of Science:

  • Machine Learning
  • Statistical Learning Theory
  • Computational Statistics

Background:

  • Selecting optimal model complexity is essential for minimizing prediction error in machine learning.
  • Existing complexity control methods include regularization, weight decay, and greedy procedures.
  • Model selection often relies on asymptotic risk estimates or resampling techniques.

Purpose of the Study:

  • To apply Vapnik-Chervonenkis (VC)-bounds for complexity control in regression problems with squared loss.
  • To empirically evaluate the performance of VC-bounds against classical model selection methods.
  • To demonstrate the advantages of VC-bounds for finite sample learning.

Main Methods:

  • Application of non-asymptotic VC-bounds to regression tasks.

Related Experiment Videos

  • Empirical study focusing on linear and penalized linear models where VC-dimension is accurately estimable.
  • Comparison of VC-bound based model selection with classical approaches across varied conditions.

    • Main Results:

    • VC-bounds provide a rigorous framework for complexity control in regression.
    • Empirical comparisons show VC-based methods outperform classical approaches in finite sample settings.
    • The effectiveness of VC-bounds is demonstrated across different noise levels, sample sizes, and function types.

    Conclusions:

    • VC-bounds offer a theoretically grounded and empirically validated method for complexity control in regression.
    • The study highlights the practical advantages of using VC-theory for model selection with finite datasets.
    • VC-based complexity control is a promising approach for improving generalization performance in machine learning.