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Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to

Charles K Fisher1, Pankaj Mehta1

  • 1Department of Physics, Boston University, Boston, MA 02215, USA.

Bioinformatics (Oxford, England)
|January 27, 2015
PubMed
Summary

We developed the Bayesian Ising Approximation (BIA) for efficient feature selection in high-dimensional regression. This method rapidly calculates feature relevance probabilities, proving effective even with thousands of genomic features.

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Area of Science:

  • Computational statistics
  • Machine learning
  • Genomic data analysis

Background:

  • Feature selection is crucial but challenging, especially for high-dimensional genomic data.
  • Identifying relevant variables is computationally intensive when features outnumber samples.

Purpose of the Study:

  • Introduce a novel, rapid approach for feature relevance calculation in L2 penalized linear regression.
  • Address the computational challenges of feature selection in high-dimensional datasets.

Main Methods:

  • Developed the Bayesian Ising Approximation (BIA) to compute posterior probabilities for feature relevance.
  • Utilized a mean field approximation to efficiently calculate the feature selection path.
  • Equated posterior probabilities to Ising model magnetizations under strong prior regularization.

Main Results:

  • Demonstrated the accuracy of BIA on simple regression problems through simulations and analytical results.
  • Applied BIA to a gene expression dataset with nearly 30,000 features, showcasing its high-dimensional applicability.
  • Highlighted the influence of feature correlations on Bayesian feature selection outcomes.

Conclusions:

  • BIA offers a computationally efficient method for feature selection in high-dimensional regression.
  • The approach is effective for analyzing large genomic datasets.
  • Understanding feature correlations is important for robust Bayesian feature selection.