Elastic Net Regularization Paths for All Generalized Linear Models

• Published in: Journal of statistical software Vol. 106; no. 1; pp. 1 - 31
• Main Authors: Tay, J Kenneth, Narasimhan, Balasubramanian, Hastie, Trevor
• Format: Journal Article
• Language: English
• Published: United States Foundation for Open Access Statistics 2023
• Subjects: coordinate descent; cox model; elastic net; generalized linear models; l1 penalty; lasso; regularization path; survival; generalized linear models; ℓ1 penalty; regularization path; Cox model; lasso; survival; coordinate descent; elastic net
• ISSN: 1548-7660; 1548-7660
• DOI: 10.18637/jss.v106.i01

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.