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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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Variable Selection via Partial Correlation.

Runze Li1, Jingyuan Liu1, Lejia Lou1

  • 1Pennsylvania State University, Xiamen University and Ernst & Young.

Statistica Sinica
|July 1, 2017
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Summary
This summary is machine-generated.

The partial correlation method for variable selection in linear regression is sensitive to normality assumptions. A new thresholded partial correlation (TPC) approach offers superior performance and selection consistency, even with ultrahigh dimensional predictors.

Keywords:
Elliptical distributionmodel selection consistencypartial correlationpartial faithfulnesssure screening propertyultrahigh dimensional linear modelvariable selection

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Partial correlation based variable selection is an alternative to regularization for linear regression.
  • Existing methods may be sensitive to normality assumptions and struggle with high-dimensional data.

Purpose of the Study:

  • To investigate the sensitivity of partial correlation methods to normality assumptions.
  • To develop a robust variable selection method for ultrahigh dimensional linear regression.

Main Methods:

  • Studied partial correlation for elliptical linear regression models.
  • Proposed a thresholded partial correlation (TPC) approach.
  • Established selection consistency for TPC with ultrahigh dimensional predictors.

Main Results:

  • The original partial correlation method shows inferior performance when marginal kurtosis deviates from normality.
  • The TPC approach demonstrates selection consistency and sure screening property.
  • TPC is competitively comparable to regularization methods.

Conclusions:

  • The TPC approach provides a robust and consistent variable selection method for linear regression.
  • TPC overcomes limitations of the original partial correlation method regarding normality assumptions and high dimensionality.