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VARIABLE SELECTION FOR HIGH DIMENSIONAL MULTIVARIATE OUTCOMES.

Tamar Sofer1, Lee Dicker2, Xihong Lin1

  • 1Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA.

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Summary
This summary is machine-generated.

This study introduces a penalized regression method for high-dimensional multivariate data, enabling accurate variable selection even with many outcomes and predictors. The approach efficiently handles within-subject correlations for robust model identification.

Keywords:
BICConsistencyCorrelationEfficiencyModel selectionMultiple outcomesOracle Estimator

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Area of Science:

  • Statistics
  • Bioinformatics
  • Computational Biology

Background:

  • High-dimensional data present challenges in multivariate regression, particularly with numerous outcomes and covariates.
  • Accounting for within-subject correlation is crucial for accurate variable selection in such settings.

Purpose of the Study:

  • To develop a penalized likelihood approach for variable selection in high-dimensional multivariate regression.
  • To address challenges posed by large numbers of outcomes and covariates, and to incorporate within-subject correlation.
  • To establish theoretical properties and computational efficiency of the proposed methods.

Main Methods:

  • Utilizing penalized likelihoods for variable selection in high-dimensional multivariate regression.
  • Employing a working precision matrix and a two-stage procedure for joint estimation of the precision matrix.
  • Implementing coordinate descent algorithm combined with graphical LASSO (GLASSO) for efficient computation.
  • Developing and validating the Bayesian Information Criterion (BIC) for tuning parameter selection.

Main Results:

  • Penalized regression coefficient estimators demonstrate consistency for model selection with arbitrary working precision matrices.
  • The proposed method exhibits oracle properties and efficiency when using the true precision matrix or a consistently estimated sparse precision matrix.
  • The coordinate descent and GLASSO algorithms provide an efficient computational procedure.
  • The BIC is shown to be consistent for model selection.

Conclusions:

  • The developed penalized regression method offers a robust approach for variable selection in high-dimensional multivariate data.
  • The method effectively handles within-subject correlations and achieves desirable statistical properties.
  • The computational strategy is efficient, and the BIC ensures reliable tuning parameter selection.
  • The approach is validated through simulations and applied to type II diabetes gene expression data.