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Comparison of model selection for regression.

Vladimir Cherkassky1, Yunqian Ma

  • 1Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA. cherkass@ece.umn.edu

Neural Computation
|June 21, 2003
PubMed
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Structural Risk Minimization (SRM) based on Vapnik-Chervonenkis (VC) theory outperforms Akaike Information Criterion (AIC) for regression model selection. This study highlights practical advantages of VC-theory for accurate model complexity estimation.

Area of Science:

  • Statistical Learning Theory
  • Machine Learning
  • Data Science

Background:

  • No consensus exists on optimal model selection methods for finite-sample estimation problems, particularly for linear estimators.
  • Classical methods like Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are widely used but may not be optimal.
  • Previous studies, such as Hastie et al. (2001), suggested Structural Risk Minimization (SRM) performs poorly and AIC offers superior predictive performance.

Purpose of the Study:

  • To empirically compare the performance of Structural Risk Minimization (SRM) against classical methods (AIC, BIC) for regression model selection.
  • To investigate the claims made by Hastie et al. (2001) regarding SRM's performance and AIC's predictive superiority.
  • To address methodological issues in SRM application and propose improvements for accurate model complexity estimation.

Related Experiment Videos

Main Methods:

  • Empirical comparison of model selection methods including SRM (based on Vapnik-Chervonenkis theory), AIC, and BIC.
  • Testing across various datasets and different regression estimator types: linear, subset selection, and k-nearest neighbor (k-NN).
  • Analysis of methodological aspects of SRM, including VC-dimension estimation, for practical application.

Main Results:

  • VC-theory-based SRM consistently outperformed AIC across all tested datasets and estimator types.
  • SRM and BIC demonstrated similar predictive performance in this study.
  • Discrepancies with previous findings are attributed to methodological drawbacks in the application and interpretation of SRM in Hastie et al. (2001).

Conclusions:

  • VC-theory-based model selection offers practical advantages and superior predictive performance compared to AIC for regression problems.
  • SRM, when applied correctly with accurate model complexity estimation, is a viable and effective model selection strategy.
  • A new practical method for estimating model complexity (VC-dimension) for k-nearest neighbors regression is proposed.