l1ratio

l1ratio is a hyperparameter used in ElasticNet models to determine the relative weight of L1 and L2 penalties in the regularization term. In libraries such as scikit-learn, l1_ratio ranges from 0 to 1, where 0 yields a pure L2 penalty (ridge), 1 yields a pure L1 penalty (lasso), and values in between form an elastic net penalty. The objective minimized typically includes a loss term plus alpha times [ l1_ratio * ||β||_1 + (1 - l1_ratio) * 0.5 * ||β||_2^2 ], with alpha controlling the overall strength of regularization.

The effect of l1ratio: The L1 component promotes sparsity by driving some coefficients to exactly zero, aiding feature selection, while the L2 component discourages large coefficients and stabilizes estimates. Adjusting l1ratio trades sparsity against coefficient shrinkage and can influence model performance and interpretability, especially when features are highly correlated.

Usage considerations: The parameter is usually tuned alongside alpha (the regularization strength) via cross-validation. In practice, a balanced l1_ratio around 0.5 serves as a reasonable starting point when feature relevance is uncertain, but domain knowledge or validation procedures may favor more sparsity (closer to 1) or smoother shrinkage (closer to 0).

Notes: ElasticNet, which incorporates l1ratio, is distinct from pure ridge or lasso. Some libraries or models expose a similar parameter for elastic-net penalties in other contexts, including logistic or linear models, typically requiring compatible solvers to converge.