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Controlling the false discoveries in LASSO.

Hanwen Huang1

  • 1Department of Epidemiology and Biostatistics University of Georgia, Athens, Georgia 30602.

Biometrics
|February 10, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a method to control the False Discovery Proportion (FDP) in LASSO regression by selecting the regularization parameter λ. This ensures reliable feature selection in high-dimensional data analysis.

Keywords:
Asymptotic distributionFactor analysis modelFalse discovery rateLASSOSparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Genomics

Background:

  • The LASSO (Least Absolute Shrinkage and Selection Operator) method is a penalized regression technique used for variable selection in high-dimensional data.
  • The regularization parameter (λ) in LASSO balances model fit and sparsity, but its direct relationship with statistical error control, like the False Discovery Proportion (FDP), is not well-established.
  • Accurate control of FDP is crucial for reliable inference, especially in fields like genomics where high-throughput data is common.

Purpose of the Study:

  • To derive a theoretical relationship between the LASSO regularization parameter (λ) and the False Discovery Proportion (FDP) of the LASSO estimator.
  • To develop a method for selecting λ to achieve a desired FDP.
  • To validate the proposed method using simulations and a real-world genomic dataset.

Main Methods:

  • Derivation of the relationship between λ and FDP based on the asymptotic distribution of the LASSO estimator as both sample size and dimension approach infinity at a fixed ratio.
  • Utilizing a factor analysis model to characterize the dependence structure within the design matrix.
  • Development of an efficient majorization-minimization algorithm for estimating FDP at a given λ.

Main Results:

  • An analytical framework is established connecting the LASSO regularization parameter (λ) to the False Discovery Proportion (FDP).
  • A method is proposed and validated for selecting λ to control FDP, demonstrating its accuracy through simulations.
  • The method's practical utility is confirmed via application to a high-throughput genomic dataset (riboflavin).

Conclusions:

  • The study provides a statistically rigorous approach to control the False Discovery Proportion in LASSO regression.
  • The derived relationship and estimation algorithm enable principled selection of the regularization parameter for reliable variable selection.
  • This methodology enhances the interpretability and trustworthiness of findings from high-dimensional data analyses, particularly in genomics.