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Bayesian group selection in logistic regression with application to MRI data analysis.

Kyoungjae Lee1, Xuan Cao2

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This study introduces a novel Bayesian logistic regression approach for high-dimensional data, achieving accurate group selection. The proposed hierarchical prior method demonstrates superior performance in simulations and real-world disease prediction tasks.

Keywords:
group spike and slab priorhigh-dimensionalstrong selection consistency

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • High-dimensional data analysis often requires identifying significant covariate groups.
  • Bayesian methods offer advantages in uncertainty quantification for model selection.
  • Existing frequentist group selection methods lack theoretical Bayesian counterparts for logistic regression.

Purpose of the Study:

  • To develop and theoretically validate a Bayesian group selection method for logistic regression in high-dimensional settings.
  • To establish the first theoretical guarantees for Bayesian group selection consistency in this context.
  • To evaluate the proposed method's performance against existing state-of-the-art techniques.

Main Methods:

  • Implementation of a hierarchical group spike and slab prior for Bayesian logistic regression.
  • Theoretical analysis to establish strong group selection consistency of the posterior distribution.
  • Simulation studies across various scenarios to assess performance.
  • Application to a real-world magnetic resonance imaging dataset for Parkinson's disease prediction.

Main Results:

  • The proposed Bayesian method achieves strong group selection consistency under mild conditions.
  • Simulation results indicate superior performance compared to existing methods.
  • The method demonstrates practical utility in predicting Parkinson's disease from MRI data.

Conclusions:

  • The study provides the first theoretical foundation for Bayesian group selection consistency in high-dimensional logistic regression.
  • The developed method is effective and outperforms current approaches.
  • The approach shows promise for applications in medical imaging and disease prediction.