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Stability Approach to Regularization Selection for Reduced-Rank Regression.

Canhong Wen1, Qin Wang1, Yuan Jiang2

  • 1International Institute of Finance, School of Management, University of Science and Technology of China.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|October 9, 2023
PubMed
Summary
This summary is machine-generated.

A new method, Stability Approach for Reduced-Rank Regression (StARS-RRR), accurately estimates the rank of coefficient matrices in regression modeling. StARS-RRR demonstrates consistent rank estimation and outperforms existing methods in simulations and a breast cancer dataset analysis.

Keywords:
Rank estimation consistencyReduced-rank regressionStability approachTuning parameter selection

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Area of Science:

  • Multivariate statistics
  • Statistical modeling
  • Bioinformatics

Background:

  • Reduced-rank regression is crucial for analyzing data with multiple responses and predictors across various scientific fields.
  • Estimating the coefficient matrix rank is key to identifying latent factors in reduced-rank regression.
  • Current rank determination methods (AIC, BIC, cross-validation) lack established theoretical guarantees.

Purpose of the Study:

  • To introduce StARS-RRR, a novel method for tuning parameter selection and rank estimation in reduced-rank regression.
  • To theoretically prove the rank estimation consistency of StARS-RRR.
  • To evaluate StARS-RRR's performance against existing methods.

Main Methods:

  • Developed StARS-RRR based on the stability approach for tuning parameter selection.
  • Utilized theoretical analysis to prove rank estimation consistency.
  • Conducted simulation studies and applied the method to a real-world breast cancer dataset.

Main Results:

  • StARS-RRR achieves consistent rank estimation.
  • Simulations show StARS-RRR provides more accurate rank estimates than AIC, BIC, and cross-validation.
  • Application to a breast cancer dataset identified relevant genetic pathways and reduced prediction error.

Conclusions:

  • StARS-RRR offers a theoretically sound and practically superior approach for rank determination in reduced-rank regression.
  • The method enhances understanding of complex biological data, such as DNA copy number variations.
  • StARS-RRR improves predictive accuracy in multivariate regression tasks.