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Optimal design of regularization term and regularization parameter by subspace information criterion.

Masashi Sugiyama1, Hidemitsu Ogawa

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This study introduces the subspace information criterion (SIC) for optimizing regularization in linear regression. SIC helps select the best regularization term and parameter, improving model generalization performance.

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Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Data Science

Background:

  • Designing effective regularization terms and parameters is crucial for linear regression model performance.
  • Generalization error estimation is key to preventing overfitting in statistical models.
  • The subspace information criterion (SIC) was previously developed as an unbiased estimator for generalization error.

Purpose of the Study:

  • To apply the subspace information criterion (SIC) to regularization learning in linear regression.
  • To utilize SIC for selecting optimal regularization terms and parameters.
  • To derive a closed-form solution for the optimal regularization parameter.

Main Methods:

  • Applying the subspace information criterion (SIC) to regularization learning.
  • Evaluating candidate regularization terms and parameters using SIC.
  • Deriving a closed-form solution for the optimal regularization parameter with a fixed term.

Main Results:

  • SIC effectively selects optimal regularization terms and parameters for linear regression.
  • A closed-form solution for the optimal regularization parameter was obtained.
  • Computer simulations confirmed the effectiveness of SIC on both artificial and real datasets.

Conclusions:

  • The subspace information criterion (SIC) provides a robust method for regularization design in linear regression.
  • SIC enhances model generalization by optimizing regularization choices.
  • This approach offers practical benefits for tuning linear regression models.