A telecom company is building a linear model to forecast customer lifetime value from almost 500 usage-based predictors. Exploratory analysis finds many predictors are strongly correlated (pairwise |ρ| > 0.8). Business stakeholders want a sparse, interpretable model that automatically removes irrelevant variables and keeps groups of correlated predictors together rather than arbitrarily dropping just one member of the group. Which regression technique, tuned with cross-validation, best meets these requirements?
Elastic net regression that mixes L1 and L2 penalties, tuned by cross-validation
Ridge regression with an L2 penalty selected by cross-validation
LASSO regression with an L1 penalty selected by cross-validation
Weighted least squares with weights inversely proportional to residual variance
Elastic net regression combines the L1 penalty of LASSO with the L2 penalty of ridge regression. The L1 component pushes small coefficients exactly to zero, delivering feature selection and sparsity. The added L2 component mitigates LASSO's tendency to pick only one variable from a set of highly correlated predictors by giving them similar shrinkage; correlated variables therefore tend to be kept or discarded as a group, which aids interpretability. Ridge regression uses only an L2 penalty-so it handles multicollinearity but never sets coefficients to zero, preventing automatic feature selection. LASSO provides sparsity but will typically keep just one variable from a correlated set, failing the grouping requirement. Weighted least squares addresses heteroscedasticity through observation weights; it does not deal with multicollinearity or perform feature selection. Hence elastic net is the most appropriate choice.
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Why does Elastic Net Regression combine L1 and L2 penalties?
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What is the difference between Elastic Net and LASSO regression in handling correlated predictors?