A Sharper Computational Tool for L₂E Regression

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Previous research by Chi and Chi (2022) explored robust structured regression under the L2E criterion.
• Existing algorithms may have limitations in convergence speed and estimation efficiency.

Purpose of the Study:

• To develop a novel, more efficient algorithm for robust structured regression estimation.
• To enhance coefficient estimation and structure recovery using advanced optimization techniques.

Main Methods:

• Adoption of the majorization-minimization (MM) principle for coefficient updates.
• Reparameterization of the model by substituting precision for scale.
• Estimation of precision via a modified Newton's method.
• Introduction of distance-to-set penalties for constrained estimation.

Main Results:

• The proposed MM algorithm demonstrates faster convergence compared to prior alternating proximal gradient descent methods.
• The reparameterization and modified Newton's method simplify and accelerate the overall estimation process.
• Distance-to-set penalties improve performance in both coefficient estimation and structure recovery.
• Simulations and a real data application validate the effectiveness of the developed tactics.

Conclusions:

• The novel algorithm offers significant improvements in speed and accuracy for robust structured regression.
• The enhanced estimation techniques provide a more robust and efficient approach to statistical modeling.
• The study contributes advanced methods for handling complex regression problems with potential applications in various data-driven fields.