Lasso and Elastic-Net Regularized Generalized Linear Models

We provide extremely efficient procedures for fitting the entire lasso or elastic-net regularization path for linear regression (gaussian), multi-task gaussian, logistic and multinomial regression models (grouped or not), Poisson regression and the Cox model. The algorithm uses cyclical coordinate descent in a path-wise fashion. Details may be found in Friedman, Hastie, and Tibshirani (2010), Simon et al. (2011), Tibshirani et al. (2012), Simon, Friedman, and Hastie (2013).

Version 3.0 is a major release with several new features, including:

  • Relaxed fitting to allow models in the path to be refit without regularization. CV will select from these, or from specified mixtures of the relaxed fit and the regular fit;
  • Progress bar to monitor computation;
  • Assessment functions for displaying performance of models on test data. These include all the measures available via cv.glmnet, as well as confusion matrices and ROC plots for classification models;
  • print methods for CV output;
  • Functions for building the x input matrix for glmnet that allow for one-hot-encoding of factor variables, appropriate treatment of missing values, and an option to create a sparse matrix if appropriate.
  • A function for fitting unpenalized a single version of any of the GLMs of glmnet.

Version 4.0 is a major release that allows for any GLM family, besides the built-in families.

Version 4.1 is a major release that expands the scope for survival modeling, allowing for (start, stop) data, strata, and sparse X inputs. It also provides a much-requested method for survival:survfit.


Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. 2010. “Regularization Paths for Generalized Linear Models via Coordinate Descent.” Journal of Statistical Software, Articles 33 (1): 1–22.

Simon, Noah, Jerome Friedman, and Trevor Hastie. 2013. “A Blockwise Descent Algorithm for Group-Penalized Multiresponse and Multinomial Regression.”

Simon, Noah, Jerome Friedman, Trevor Hastie, and Robert Tibshirani. 2011. “Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent.” Journal of Statistical Software, Articles 39 (5): 1–13.

Tibshirani, Robert, Jacob Bien, Jerome Friedman, Trevor Hastie, Noah Simon, Jonathan Taylor, and Ryan Tibshirani. 2012. “Strong Rules for Discarding Predictors in Lasso-Type Problems.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74 (2): 245–66.

Kenneth Tay, J, Narasimhan, Balasubramanian, Hastie, Trevor. 2023. “Elastic Net Regularization Paths for All Generalized Linear Models.” Journal of Statistical Software, Articles 106 (1): 1–31.

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Last Published

August 22nd, 2023

Functions in glmnet (4.1-8)