Forward stagewise regression and the monotone lasso

Simple item page
dc.creatorHastie, Trevor
dc.creatorTaylor, Jonathan
dc.creatorTibshirani, Robert
dc.creatorWalther, Guenther
dc.date2007-05-02
dc.date.accessioned2026-07-07T08:01:56Z
dc.date.available2026-07-07T08:01:56Z
dc.descriptionWe consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a small modification, solves the lasso regression problem. Here we give an analogous result for incremental forward stagewise regression, showing that it solves a version of the lasso problem that enforces monotonicity. One consequence of this is as follows: while lasso makes optimal progress in terms of reducing the residual sum-of-squares per unit increase in $L_1$-norm of the coefficient $β$, forward stage-wise is optimal per unit $L_1$ arc-length traveled along the coefficient path. We also study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the lasso and forward stagewise procedures in a simulation study involving a large number of correlated predictors.
dc.descriptionPublished at http://dx.doi.org/10.1214/07-EJS004 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0705.0269
dc.identifierhttp://arxiv.org/abs/0705.0269
dc.identifierElectronic Journal of Statistics 2007, Vol. 1, 1-29
dc.identifierdoi:10.1214/07-EJS004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129076
dc.subjectStatistics Theory
dc.subject62J99 (Primary) 62J07 (Secondary)
dc.titleForward stagewise regression and the monotone lasso
dc.typetext

Files

Collections

arXiv