Berwin's Problem

The title Lasso has been suggested by Tibshirani 6] as a colourful description of a technique for variable selection which requires the minimization of a sum of squares subject to an l1 bound on the solution components. This bound then has the role of the selection parameter. Here a descent method for solving the constrained problem is formulated, a homotopy method in which the constraint bound becomes the homo-topy parameter is developed to completely describe the possible selection regimes, and it is suggested that modiied Gram-Schmidt applied to the augmented design matrix provides an eeective base for implementing the suggested algorithms.