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Elastic Net Regularization Paths for All Generalized Linear Models.

J Kenneth Tay¹, Balasubramanian Narasimhan², Trevor Hastie²

¹Department of Statistics, Stanford University, 390 Jane Stanford Way, Stanford, California 94305, United States of America.

Journal of Statistical Software

|May 4, 2023

Summary

This summary is machine-generated.

The elastic net regularization method now supports a wider range of generalized linear and Cox models, including complex survival data. This advancement offers more flexible tools for supervised learning and model performance evaluation.

Keywords:

Cox model coordinate descent elastic net generalized linear models lasso regularization path survival ℓ1 penalty

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Area of Science:

Statistical modeling
Machine learning
Computational statistics

Background:

Lasso and elastic net are established regularized regression techniques.
Previous algorithms efficiently computed elastic net paths for OLS, logistic, and multinomial logistic regression.
Extensions existed for Cox models with right-censored data.

Purpose of the Study:

To extend elastic net regularization to a broader class of models.
To incorporate Cox models with interval-censored data and strata.
To introduce a simplified relaxed lasso and utility functions for model evaluation.

Main Methods:

Algorithm extension for generalized linear models (GLMs).
Adaptation for Cox models with start-stop data and strata.
Implementation of a simplified relaxed lasso algorithm.
Development of model performance assessment utilities.

Main Results:

Successful extension of elastic net regularization to all GLM families.
Capability to handle Cox models with interval-censored data and strata.
Availability of a simplified relaxed lasso.
Inclusion of practical functions for model performance evaluation.

Conclusions:

The elastic net framework is now more versatile, covering a wider array of statistical models.
These extensions provide enhanced capabilities for analyzing complex and censored survival data.
The updated methods and utilities facilitate more robust supervised learning and model selection.