Robust reduced-rank regression.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• High-dimensional multivariate regression requires dimension reduction via low-rank coefficient matrices for efficient parameter estimation.
• Existing reduced-rank methods are vulnerable to outliers, distorting the low-rank structure and compromising accuracy.
• Robustness is crucial for reliable analysis in the presence of corrupted data.

Purpose of the Study:

• To develop a robust reduced-rank regression approach for joint modeling and outlier detection in high-dimensional data.
• To generalize and unify popular robust multivariate regression techniques.
• To improve prediction accuracy by simultaneously addressing rank reduction and outlier identification.

Main Methods:

• Formulation as regularized multivariate regression with sparse mean-shift parameterization.
• Development of an efficient thresholding-based iterative optimization procedure.
• Non-asymptotic robust theoretical analysis to guarantee convergence and statistical accuracy.

Main Results:

• The proposed algorithm is guaranteed to converge to a statistically accurate solution.
• Joint rank reduction and outlier detection significantly enhance prediction accuracy.
• Redescending -functions and convex regularization achieve minimax optimal error rates.

Conclusions:

• The developed robust reduced-rank regression method offers a powerful tool for high-dimensional data analysis.
• The approach effectively handles outliers, leading to more reliable and accurate models.
• The method demonstrates superior performance in both simulated and real-world datasets.