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Group variable selection via ℓp,0 regularization and application to optimal scoring.

Duy Nhat Phan1, Hoai An Le Thi2

  • 1Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam.

Neural Networks : the Official Journal of the International Neural Network Society
|July 19, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a DC programming approach for group sparsity using ℓp,0-norm regularization. The method efficiently selects relevant variable groups for interpretable data representation.

Keywords:
regularizationDC approximationDC programmingDCAGroup variable selectionOptimal scoring

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Area of Science:

  • Statistics
  • Machine Learning
  • Optimization

Background:

  • Variable selection is crucial in statistical modeling.
  • Enforcing group sparsity aids in model interpretability and dimensionality reduction.

Purpose of the Study:

  • To develop and investigate a DC (Difference of Convex functions) approximation approach for ℓp,0-norm regularization.
  • To apply this method for group variable selection in optimal scoring problems.

Main Methods:

  • Utilized DC programming and the DC Algorithm (DCA) to solve the ℓp,0-norm regularization problem.
  • Demonstrated the equivalence between the original and approximate problems under suitable parameters.

Main Results:

  • Successfully implemented DC programming and DCA for group variable selection.
  • Achieved sparsity by selecting identical features across discriminant vectors using ℓp,0-regularization.
  • Generated sparse discriminant vectors for interpretable low-dimensional data representation.

Conclusions:

  • The proposed DC approximation approach is efficient for group sparsity.
  • The method provides effective group variable selection for optimal scoring.
  • Experimental results confirm the efficiency on simulated and real datasets.