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A Scalable Empirical Bayes Approach to Variable Selection in Generalized Linear Models.

Haim Y Bar1, James G Booth2, Martin T Wells2

  • 1Department of Statistics University of Connecticut, Storrs CT, 06269, USA.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|June 26, 2024
PubMed
Summary
This summary is machine-generated.

A novel empirical Bayes method enhances variable selection for generalized linear models. This computationally efficient algorithm effectively handles numerous explanatory variables, improving model accuracy.

Keywords:
EM algorithmFeature selectionGeneralized linear mixed modelHigh dimensional dataMixture modelSparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Computational Biology

Background:

  • Variable selection is crucial for building accurate generalized linear models (GLMs).
  • Traditional methods struggle with a large number of potential explanatory variables, exceeding the number of responses.
  • Existing Bayesian approaches can be computationally intensive and slow to converge.

Purpose of the Study:

  • To develop a scalable empirical Bayes approach for variable selection in GLMs.
  • To address the challenge of high-dimensional explanatory variables where predictors may far outnumber observations.
  • To create a computationally efficient algorithm with faster convergence than simulation-based methods.

Main Methods:

  • A three-component mixture model for coefficients in the linear predictor.
  • Modeling coefficients as random effects (positive, negative, or no effect).
  • Utilizing a Generalized Alternating Maximization algorithm for parameter estimation.

Main Results:

  • The proposed algorithm scales effectively to very large numbers of explanatory variables.
  • The number of estimated parameters remains constant, irrespective of the number of predictors.
  • Demonstrated significantly faster convergence compared to simulation-based fully Bayesian methods.

Conclusions:

  • The new empirical Bayes approach offers an efficient and scalable solution for variable selection in GLMs.
  • This method is particularly advantageous for high-dimensional datasets.
  • The algorithm provides a computationally superior alternative to existing Bayesian techniques.