A1342
Title: A computational note on the penalized correlation-based estimators in linear and generalized linear models
Authors: Mina Norouzirad - Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (Portugal) [presenting]
Marta Lopes - Department of Mathematics NOVA School of Science and Technology (Portugal)
Tomas Bandeira - NOVA University Lisbon (Portugal)
Ricardo Moura - Center for Mathematics and Applications (Portugal)
Abstract: Penalized regression methods such as ridge, lasso, and elastic net have become standard tools in statistical modeling, yet they do not explicitly account for correlations among explanatory variables. This limitation may reduce performance in the presence of strong multicollinearity, leading to unstable or biased coefficient estimates. To address this issue, a prior study proposed a correlation-based penalty that incorporates dependence structures directly into the estimation process. Despite its theoretical appeal, the practical implementation of this estimator is challenging, particularly in high-dimensional settings where the number of predictors can exceed the sample size. The purpose is to revisit correlation-based penalized regression from a computational perspective. The aim is to investigate efficient algorithms for estimating this estimator, with particular attention to numerical stability, and to compare their computational time and performance across different scenarios. The focus is on exploring approaches that may render the estimator feasible and useful in practice, especially in high-dimensional contexts. The ultimate objective is to provide a practical implementation, thereby extending the toolbox of penalized regression methods available for linear and generalized linear models.
