Coefficient pairing with centralized regularization for structured sparsity.

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Sparse linear regression faces challenges with highly correlated predictors and unobserved coefficient groupings.
• Existing methods struggle to effectively incorporate latent group structures into regularization.
• Accurate variable selection and coefficient estimation are crucial for high-dimensional data.

Purpose of the Study:

• To propose a novel structured sparsity penalty, coefficient-paired estimation with centralized regularization (CECR).
• To enable group-aware shrinkage and preserve sparsity in linear regression models.
• To address challenges posed by strong predictor correlation and latent coefficient group structures.

Main Methods:

• Developed CECR, a penalty that pairs coefficients with learned group centers for joint shrinkage.
• Employed an efficient iterative coordinate descent algorithm for model optimization.
• Established theoretical guarantees including variable selection consistency and estimation accuracy.

Main Results:

• CECR demonstrates improved support recovery and prediction performance in simulations across various group patterns and correlation levels.
• The method effectively handles latent group structures without requiring prior group labels.
• CECR achieved lower tracking error in a Nasdaq 100 index tracking application compared to baseline regularizers.

Conclusions:

• CECR offers a promising approach for structured sparsity in high-dimensional linear regression.
• The method shows potential for large-scale predictive modeling, parameter sharing, and pruning.
• CECR enhances model interpretability and predictive power by leveraging latent coefficient structures.