The Iso-lambda Descent Algorithm for the LASSO

Following the introduction by Tibshirani of the LASSO tech- nique for feature selection in regression, two algorithms were proposed by Osborne et al. for solving the associated problem. One is an homo- topy method that gained popularity as the LASSO modication of the LARS algorithm. The other is a nite-step descent method that follows a path on the constraint polytope, and seems to have been largely ignored. One of the reason may be that it solves the constrained formulation of the LASSO, as opposed to the more practical regularized formulation. We give here an adaptation of this algorithm that solves the regularized problem, has a simpler formulation, and outperforms state-of-the-art al- gorithms in terms of speed.