Coefficient pairing with centralized regularization for structured sparsity

Sparse linear regression is widely used, yet challenges remain under strong predictor correlation and when coefficients exhibit latent group structure not implied by covariate correlation. We propose coefficient-paired estimation with centralized regularization (CECR), a structured sparsity penalty that pairs each coefficient with a learned group center to enable group-aware shrinkage while preserving sparsity. CECR jointly learns coefficients and centers without prior group labels and is solved by an efficient iterative coordinate descent algorithm. We establish variable selection and estimation consistency, finite sample error bounds, and asymptotic normality as the dimension and sample size increase. Simulations across diverse coefficient group patterns and correlation regimes show improved support recovery and prediction relative to strong baselines. In a Nasdaq 100 index tracking application, CECR yields lower tracking error than competing regularizers, indicating promise for large scale predictive modeling and for parameter sharing and pruning in high dimensional models.