# 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`

.

## References

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.
https://doi.org/10.18637/jss.v033.i01.

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. https://doi.org/10.18637/jss.v039.i05.

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.
https://doi.org/10.1111/j.1467-9868.2011.01004.x.

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. https://doi.org/10.18637/jss.v106.i01.