Principal component-guided sparse reduced-rank regression

2026-01-12

AI Summary

This work proposes a novel approach that integrates principal component–guided sparse regularization (pcLasso) into the reduced-rank regression framework, addressing a key limitation of existing methods which struggle to simultaneously exploit the principal component structure and group structure of predictors while effectively biasing regression coefficients toward high-variance principal component directions. By explicitly incorporating predictor principal component orientations, group information, and inter-response correlations, the proposed method overcomes constraints inherent in conventional models, enhancing both predictive accuracy and model interpretability. Extensive numerical simulations and real-data analyses demonstrate the substantial advantages of this approach in terms of prediction performance and explanatory power.

Technology Category

Machine Learning: Dimensionality Reduction/Feature SelectionReasoning under Uncertainty: Graphical ModelsComputer Vision: Learning & Optimization for CV

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and model interpretability, several regularized reduced-rank regression methods have been proposed. However, these existing methods cannot bias the regression coefficients toward the leading principal component directions while accounting for the correlation structure among explanatory variables. In addition, when the explanatory variables exhibit a group structure, the correlation structure within each group cannot be adequately incorporated. To overcome these limitations, we propose a new method that introduces pcLasso into the reduced-rank regression framework. The proposed method improves predictive accuracy by accounting for the correlation among response variables while strongly biasing the matrix of regression coefficients toward principal component directions with large variance. Furthermore, even in settings where the explanatory variables possess a group structure, the proposed method is capable of explicitly incorporating this structure into the estimation process. Finally, we illustrate the effectiveness of the proposed method through numerical simulations and real data application.

Problem

• reduced-rank regression
• principal component
• group structure
• correlation structure
• regression coefficients

Innovation

• reduced-rank regression
• pcLasso
• principal component bias
• group structure
• regularization