LASSO

It is also a shrinkage method like Ridge.  Lasso estimates are defined as

We re-parametrize the constant β₀ by standardizing the predictors and then fit a model without intercept. We can write lasso problem in equivalent Lagrangian form,

The L₂ ridge penalty is replaced by L₁ lasso penalty. Because of this L₁, the solution becomes non-linear in y_i. Computing the lasso solution is a quadratic programming problem. Lasso does a continuous type of subset selection.