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A polynomial algorithm for best-subset selection problem.

Junxian Zhu1, Canhong Wen2, Jin Zhu1

  • 1School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong 510275, China.

Proceedings of the National Academy of Sciences of the United States of America
|December 17, 2020
PubMed
Summary
This summary is machine-generated.

We developed a new polynomial algorithm for best-subset selection to improve linear model prediction accuracy. This method efficiently identifies the optimal subset of predictors, even with unknown model sparsity.

Keywords:
best-subset selectionhigh dimensionalsplicing

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Area of Science:

  • Statistics
  • Computer Science
  • Applied Mathematics

Background:

  • Best-subset selection is crucial for enhancing linear model prediction accuracy in regression analysis.
  • It has broad applications across various research fields, including computer science and medicine.
  • Finding the optimal subset of predictors remains a significant challenge.

Purpose of the Study:

  • To introduce a novel polynomial algorithm for efficient and accurate best-subset selection.
  • To address the challenge of identifying the true sparsity level in linear models.
  • To ensure the algorithm achieves stable and optimal solutions.

Main Methods:

  • A polynomial algorithm employing sequencing and splicing techniques.
  • Development of a novel information criterion for sparsity level selection.
  • Analysis of algorithm stability and convergence properties under mild conditions.

Main Results:

  • The algorithm achieves a stable solution in finite steps for fixed but unknown sparsity levels.
  • The proposed information criterion successfully identifies the true sparsity level with high probability.
  • When stable, the algorithm's solution is shown to be the oracle estimator with probability one.

Conclusions:

  • The introduced polynomial algorithm provides an effective solution for best-subset selection.
  • The method demonstrates high accuracy in identifying optimal predictor subsets and model sparsity.
  • Numerical studies confirm the algorithm's practical utility and performance.