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Bayesian sparse reduced rank multivariate regression.

Gyuhyeong Goh1, Dipak K Dey2, Kun Chen2

  • 1Department of Statistics, Kansas State University, Manhattan, KS 66506, United States.

Journal of Multivariate Analysis
|October 10, 2017
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Summary
This summary is machine-generated.

This study introduces a Bayesian method for sparse and low-rank multivariate regression, enabling simultaneous dimension reduction and variable selection. The approach effectively estimates coefficient matrices and provides credible regions for robust statistical inference.

Keywords:
BayesianLow rankPosterior consistencyRank reductionSparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Multivariate regression is crucial for modern statistical problems involving complex datasets.
  • Sparse and low-rank coefficient matrices offer insights into underlying data structures.
  • Existing methods may not simultaneously address sparsity, low-rank properties, and variable selection.

Purpose of the Study:

  • To develop a unified Bayesian approach for sparse and low-rank multivariate regression.
  • To enable simultaneous estimation of the coefficient matrix, credible region calculation, and hyperparameter tuning.
  • To facilitate dimension reduction, predictor selection, and response selection.

Main Methods:

  • A Bayesian framework is employed for multivariate regression analysis.
  • A novel sparse and low-rank prior is introduced for the coefficient matrix.
  • Marginal likelihood is used for hyperparameter selection, optimizing posterior probability.

Main Results:

  • The proposed method effectively estimates sparse and low-rank coefficient matrices.
  • Simultaneous rank reduction, predictor selection, and response selection are achieved.
  • Posterior consistency is established, demonstrating asymptotic behavior.

Conclusions:

  • The developed Bayesian method provides a unified approach for sparse and low-rank multivariate regression.
  • The method is effective in statistical inference, dimension reduction, and variable selection.
  • The approach shows efficacy in simulations and a real-world application in yeast cell cycle data analysis.