Journal Article

L1-regularization path algorithm for generalized linear models

Park, Mee Young, Hastie, Trevor

2007

Overview

We introduce a path following algorithm forL_{1}$-regularized generalized linear models. TheL_{1}$-regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on theL_{1}$-norm of the coefficients, in a manner that is less greedy than forward selection-backward deletion. The generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor-corrector method of convex optimization. Selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths; we suggest intuitive and flexible strategies for choosing appropriate values. We demonstrate the implementation with several simulated and real data sets.

• Publisher: Blackwell Publishing Ltd,Blackwell Publishers,Blackwell,Oxford University Press
• Subject: Algorithms / Arc length / Coefficients / Data analysis / data collection / Datasets / Exact sciences and technology / General topics / Generalized linear model / Generalized linear models / Genetic vectors / Heart diseases / Lasso / Linear analysis / Linear inference, regression / Linear models / Linear programming / Logistic regression / Mathematical functions / Mathematical methods / Mathematics / Numerical analysis / Numerical analysis. Scientific computation / Numerical linear algebra / Optimization / Parametric inference / Path algorithm / Predictor corrector methods / Predictor-corrector method / Probability and statistics / Regularization / Sciences and techniques of general use / Simulation / Statistical methods / Statistical models / Statistics / Studies / Variable coefficients / Variable selection