# Elastic Net Regularization Paths for All Generalized Linear Models

“Elastic Net Regularization Paths for All Generalized Linear Models” (2023), by Jingyi Kenneth Tay et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Jingyi Kenneth Tay, Balasubramanian Narasimhan, Trevor Hastie
- Published: January 1, 2023
- Field: Mathematics
- DOI: https://doi.org/10.18637/jss.v106.i01
- Free PDF: https://www.jstatsoft.org/index.php/jss/article/download/v106i01/4459

## Abstract

The lasso and elastic net are popular regularized regression models for supervised learning. Friedman, Hastie, and Tibshirani (2010) introduced a computationally efficient algorithm for computing the elastic net regularization path for ordinary least squares regression, logistic regression and multinomial logistic regression, while Simon, Friedman, Hastie, and Tibshirani (2011) extended this work to Cox models for right-censored data. We further extend the reach of the elastic net-regularized regression to all generalized linear model families, Cox models with (start, stop] data and strata, and a simplified version of the relaxed lasso. We also discuss convenient utility functions for measuring the performance of these fitted models.

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