Elastic Net Regression
Elastic Net Regularized Regression · Also known as: elastic net, EN regression, L1+L2 regularized regression, combined lasso-ridge regression
Elastic net regression combines the L1 (lasso) and L2 (ridge) penalties into a single regularized regression framework. Controlled by a mixing parameter alpha and a shrinkage strength lambda, it can simultaneously select variables and handle correlated predictors — overcoming key limitations of pure lasso and pure ridge applied alone.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use elastic net when you have more predictors than observations (p > n), when predictors are highly correlated (collinear groups), or when you suspect only a subset of predictors is truly relevant. It is the preferred choice over plain lasso when correlated predictors must be retained together rather than arbitrarily dropped. Do not use elastic net when you need unbiased coefficient estimates for causal interpretation (regularization shrinks coefficients toward zero), when your primary goal is inference on specific predictors rather than prediction, or when n is large relative to p and predictors are uncorrelated (OLS is sufficient and more interpretable in that setting).
Strengths & limitations
- Handles p >> n settings where OLS is infeasible.
- Performs automatic variable selection (coefficients set exactly to zero) while also grouping correlated predictors, unlike pure lasso.
- More stable than lasso when predictors are highly correlated — correlated features tend to be selected or dropped together.
- Flexible: alpha tunes the lasso-ridge balance to match the data structure.
- Convex objective ensures a global optimum, and efficient algorithms (coordinate descent) make it scalable to large datasets.
- Introduces bias: shrinkage pulls all coefficients toward zero, so elastic net estimates are biased even when the true model is linear.
- Requires selection of two hyperparameters (lambda, alpha), increasing the cross-validation computational burden.
- Post-selection inference is non-trivial; standard confidence intervals do not apply without correction.
- When predictors are uncorrelated and the sample is large, OLS is simpler and provides unbiased estimates.
Frequently asked
How is elastic net different from lasso and ridge?
Lasso uses only the L1 penalty (sets some coefficients to zero, but is unstable with correlated predictors). Ridge uses only the L2 penalty (shrinks all coefficients but never sets them to zero). Elastic net blends both: the alpha parameter controls the mix. When 0 < alpha < 1, you get simultaneous variable selection and grouping of correlated predictors — the main advantage over either penalty alone.
How do I choose alpha and lambda?
Use cross-validation. In practice, run a grid search over a sequence of alpha values (e.g., 0, 0.25, 0.5, 0.75, 1.0) and, for each alpha, over a log-spaced sequence of lambda values. Select the (alpha, lambda) pair that minimises the cross-validated prediction error. The glmnet package in R and scikit-learn in Python implement this efficiently.
Do I need to standardize my predictors?
Yes. The L1 and L2 penalties penalize raw coefficient magnitudes, so predictors measured on larger scales will be penalized more heavily unless you standardize. Most software (glmnet, scikit-learn ElasticNet) standardizes internally by default, but verify this for your tool and back-transform coefficients if needed for interpretation.
Can I use elastic net for classification?
Yes. Replacing the squared-error loss with a logistic loss yields elastic net logistic regression, which performs penalized binary or multinomial classification with automatic variable selection. The same alpha and lambda tuning approach applies.
Are the coefficient estimates from elastic net unbiased?
No. Regularization intentionally introduces bias to reduce variance and prevent overfitting. If unbiased estimates are essential (e.g., for causal claims), consider post-selection OLS on the selected variables, or use debiased lasso / selective inference methods.
Sources
- Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301-320. DOI: 10.1111/j.1467-9868.2005.00503.x ↗
- Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer. ISBN: 978-0387848570
How to cite this page
ScholarGate. (2026, June 3). Elastic Net Regularized Regression. ScholarGate. https://scholargate.app/en/statistics/elastic-net-regression
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Lasso RegressionMachine learning↔ compare
- OLS RegressionEconometrics↔ compare
- Quantile RegressionEconometrics↔ compare
- Regularized Logistic RegressionMachine learning↔ compare
- Ridge RegressionMachine learning↔ compare
- Robust RegressionStatistics↔ compare