Stagewise Lasso

Abstract

Many statistical machine learning algorithms minimize either an empirical loss function as in AdaBoost, or a penalized empirical loss as in Lasso or SVM. A single regularization tuning parameter controls the trade-off between fidelity to the data and generalizability, or equivalently between bias and variance. When this tuning parameter changes, a regularization "path" of solutions to the minimization problem is generated, and the whole path is needed to select a tuning parameter to optimize the prediction or interpretation performance. Algorithms such as homotopy-Lasso or LARS-Lasso and Forward Stagewise Fitting (FSF) (aka e-Boosting) are of great interest because of their resulted sparse models for interpretation in addition to prediction.