Elastic Net Regularization Paths for All Generalized Linear Models

TL;DR

This paper extends elastic net regularization paths to all generalized linear models, Cox models with complex data, and introduces utility functions for model performance assessment, broadening the applicability of elastic net methods.

Contribution

It provides a unified algorithm for elastic net regularization paths across all GLM families, Cox models with advanced data structures, and a simplified relaxed lasso, enhancing computational efficiency and versatility.

Findings

Extended elastic net to all GLM families.

Supported Cox models with complex data structures.

Introduced utility functions for model performance measurement.

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.