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Ryan Miller1, Patrick Breheny2

  • 1Department of Mathematics, Grinnell College, Grinnell, Iowa, USA.

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Summary
This summary is machine-generated.

We introduce a new method to assess the reliability of variable selection in penalized regression models like the lasso. This approach helps estimate the false discovery rate, improving confidence in model findings for high-dimensional data analysis.

Keywords:
false discovery rateshigh-dimensional datahigh-dimensional modelslassopenalized regression

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Area of Science:

  • Statistics
  • Computational Biology
  • Bioinformatics

Background:

  • Penalized regression, including the lasso, is widely used for high-dimensional data analysis due to its variable selection capabilities.
  • Assessing the reliability of variable selections in penalized regression remains a critical challenge.
  • Existing methods may not adequately address the potential for high false discovery rates, especially with cross-validation model selection.

Purpose of the Study:

  • To propose a novel method for calculating local false discovery rates (LFDRs) for variables selected by penalized regression models.
  • To provide a reliable measure for assessing individual feature significance and the overall model's false discovery rate.
  • To enhance the interpretability and trustworthiness of penalized regression models in high-dimensional settings.

Main Methods:

  • Developed a method to compute LFDRs for variables within penalized regression frameworks, inspired by large-scale hypothesis testing.
  • The method is applicable across various regularization levels and penalized likelihoods, including generalized linear models and Cox regression.
  • Evaluated the approach using simulations and comparisons with existing inferential methods and univariate LFDRs.

Main Results:

  • The proposed LFDR method effectively quantifies the reliability of variable selections in penalized regression.
  • Demonstrated the method's validity and its ability to identify potentially unreliable selections, even in models with few significant features.
  • The approach is flexible, accommodating diverse penalties like minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD).

Conclusions:

  • The LFDR method offers a robust tool for evaluating variable selection reliability in penalized regression.
  • This technique is crucial for improving the accuracy and interpretability of models analyzing complex, high-dimensional datasets.
  • Practical application in gene expression data analysis highlights its utility in biological research and clinical applications.