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Bayesian Distance Weighted Discrimination.

Eric F Lock1

  • 1Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55446, USA.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|December 5, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian framework for Distance Weighted Discrimination (DWD), a method for high-dimensional data classification. The new approach enables robust statistical inference, uncertainty assessment, and automated parameter tuning for DWD models.

Keywords:
Cancer genomicsdistance weighted discriminationhigh-dimensional dataprobabilistic classification

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Distance Weighted Discrimination (DWD) is effective for high-dimensional data classification.
  • DWD lacks a model-based framework for statistical inference.
  • Existing optimization techniques efficiently solve DWD's objective function.

Purpose of the Study:

  • To establish a Bayesian framework for Distance Weighted Discrimination (DWD).
  • To enable statistical inference, uncertainty quantification, and automated tuning for DWD.
  • To demonstrate the utility of Bayesian DWD in classification tasks.

Main Methods:

  • DWD is framed as identifying the mode of a Bayesian posterior distribution.
  • A specific link function and a shrinkage-inducing prior are utilized.
  • A Markov Chain Monte Carlo (MCMC) algorithm is developed for posterior simulation.

Main Results:

  • The Bayesian DWD posterior is shown to be asymptotically normal.
  • The mean and covariance matrix of the limiting distribution are derived.
  • Simulations and a breast cancer genomics application showcase the framework's benefits.

Conclusions:

  • Bayesian DWD provides well-calibrated posterior probabilities and quantifies coefficient uncertainty.
  • The framework improves power through semi-supervised learning and automates penalty parameter selection.
  • R code is available for implementing Bayesian DWD.