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Kernel Knockoffs Selection for Nonparametric Additive Models.

Xiaowu Dai1, Xiang Lyu1, Lexin Li1

  • 1University of California, Berkeley.

Journal of the American Statistical Association
|December 25, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new kernel knockoffs method for nonparametric additive models, ensuring false discovery rate (FDR) control for any sample size. The method offers improved variable selection in statistical modeling.

Keywords:
False discovery rateKnockoffsNonparametric additive modelsReproducing kernel Hilbert spaceSubsamplingVariable selection

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Area of Science:

  • Statistics
  • Machine Learning

Background:

  • Nonparametric additive models offer a balance of flexibility and interpretability.
  • Existing variable selection methods often fail to control the false discovery rate (FDR) without large sample sizes.
  • The knockoff framework provides a robust approach to FDR control but has limited applicability to nonparametric models.

Purpose of the Study:

  • To develop a novel knockoff-based variable selection procedure for nonparametric additive models.
  • To ensure finite sample FDR control for nonparametric variable selection.
  • To enhance the power of variable selection in nonparametric settings.

Main Methods:

  • Integration of knockoffs with subsampling for enhanced stability.
  • Application of random feature mapping for nonparametric function approximation.
  • Development of a kernel knockoffs selection procedure tailored for additive models.

Main Results:

  • The proposed method guarantees FDR control across all sample sizes.
  • Achieves asymptotic power approaching one as sample size increases.
  • Demonstrated efficacy through simulations and comparisons with existing methods.

Conclusions:

  • The novel kernel knockoffs procedure effectively addresses limitations in nonparametric variable selection.
  • Provides a statistically rigorous method for FDR control in nonparametric additive models.
  • Offers a valuable contribution to statistical inference and machine learning methodologies.