Elastic Net Regularization Paths for All Generalized Linear Models

2023/01/01 by J. Kenneth Tay, Balasubramanian Narasimhan, Trevor Hastie · 20 citations
Mathematics · #Advanced Statistical Methods and Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.18637/jss.v106.i01

openalex publication_date 2023/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• Cox's Regression Model for Counting Processes: A Large Sample Study
• Julia: A Fresh Approach to Numerical Computing
• Generalized Linear Models
• Ridge Regression: Biased Estimation for Nonorthogonal Problems

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