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A Consistent Information Criterion for Support Vector Machines in Diverging Model Spaces.

Xiang Zhang1, Yichao Wu1, Lan Wang2

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.

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Summary
This summary is machine-generated.

This study provides theoretical support for the support vector machine information criterion (SMIC) in feature selection. A modified SMIC ensures model selection consistency, even with a rapidly increasing number of features.

Keywords:
Bayesian Information CriterionDiverging Model SpacesFeature SelectionSupport Vector Machines

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Area of Science:

  • Statistics
  • Machine Learning
  • Computational Biology

Background:

  • Information criteria are vital for model selection with established theoretical properties.
  • The support vector machine information criterion (SMIC) was proposed for feature selection in classification but lacked theoretical justification.

Purpose of the Study:

  • To provide theoretical justifications for the support vector machine information criterion (SMIC).
  • To establish model selection consistency for SMIC in both fixed and diverging model spaces.

Main Methods:

  • Derivation of a uniform convergence rate for the support vector machine solution.
  • Modification of SMIC to achieve model selection consistency.
  • Monte Carlo simulations and analysis of a gene selection problem.

Main Results:

  • Demonstrated model selection consistency for a modified SMIC, even with features growing exponentially with sample size.
  • Established theoretical guarantees for SMIC in feature selection.
  • Validated finite-sample performance through simulations and a real-world gene selection task.

Conclusions:

  • The modified support vector machine information criterion offers theoretical justification and consistent model selection.
  • This work extends the applicability of information criteria to complex feature selection scenarios in machine learning.
  • The findings are applicable to optimizing tuning parameters in penalized support vector machine methods.