glmnet

glmnet is a software package for fitting generalized linear models with elastic-net regularization. It computes the entire regularization path for a sequence of penalty parameters lambda using a fast coordinate-descent algorithm, enabling efficient fitting even when the number of predictors p is large. The package supports multiple model families, including Gaussian (linear regression), binomial (logistic regression), Poisson, multinomial, and Cox proportional hazards models, covering a broad range of regression and classification tasks.

Regularization is controlled by alpha in [0,1], where alpha=1 corresponds to lasso (L1 penalty) and alpha=0 to ridge (L2 penalty). Intermediate values provide elastic-net penalties. Predictors are standardized by default and an intercept is included unless requested otherwise. The lambda sequence can be chosen automatically or supplied by the user. The method is well suited to high-dimensional data and can handle correlated predictors due to the ridge component in the elastic-net penalty.

The glmnet function returns an object containing the fitted coefficients for all lambda values, the intercepts, the lambda grid, and fit diagnostics such as the deviance and degrees of freedom. Predictions and plotting can be performed with predict.glmnet and plot.glmnet, and cross-validation can be conducted with cv.glmnet to select lambda_min or lambda_1se.

glmnet is open-source, with code primarily in Fortran and an R interface, and is widely used in statistics and machine learning for regularized regression and classification. It originated from the work of Jerome Friedman, Trevor Hastie, and Robert Tibshirani and is distributed under an open-source license.