A new approach to variable selection in least squares problems

The title Lasso has been suggested by Tibshirani 7 as a colourful name for a technique of variable selection which requires the minimization of a sum of squares subject to an ll bound r; on the solution. This forces zero components in the minimizing solution for small values of r;. Thus this bound can function as a selection parameter. This paper makes two contributions to computational problems associated with implementing the Lasso: (1) a com- pact descent method for solving the constrained problem for a particular value of r; is formulated, and (2) a homotopy method, in which the constraint bound r; becomes the homotopy parameter, is developed to completely describe the possible selection regimes. Both algorithms have a finite termination property.