Reduced rank regression via adaptive nuclear norm penalization

Area of Science:

• Statistics
• Machine Learning
• Genetics

Background:

• High-dimensional data presents challenges for traditional multivariate regression.
• Low-rank matrix approximation is crucial for dimensionality reduction.

Purpose of the Study:

• To develop a novel reduced rank estimation method for high-dimensional multivariate regression.
• To introduce an adaptive nuclear norm penalization approach for improved matrix approximation.

Main Methods:

• Proposed an adaptive nuclear norm defined as a weighted sum of singular values.
• Developed a non-convex penalized regression method yielding a global optimum.
• Utilized adaptively soft-thresholded singular value decomposition for efficient computation.

Main Results:

• The proposed method achieves a continuous solution path and computational efficiency.
• Established rank consistency and performance bounds for the estimator in high dimensions.
• Demonstrated efficacy through simulation studies and a genetic data application.

Conclusions:

• The adaptive nuclear norm approach offers an effective and efficient solution for high-dimensional regression.
• The method provides theoretical guarantees for rank consistency and prediction accuracy.
• Validated through practical applications, highlighting its utility in fields like genetics.