3.3 Lasso (L1, α = 1)🔗ℹ

The lasso is the elastic net at α = 1: a pure L1 penalty. Where ridge shrinks every coefficient but keeps them all, the lasso performs variable selection — it drives coefficients exactly to zero, and more of them as λ grows. It is the model you reach for when you believe only a few predictors matter and you want the fit to say which.

Using the same fixture — relevant x₁, x₂ and the irrelevant x₃ = x₁² — a modest λ selects x₃ out entirely (its coefficient is 0.0) while keeping the two real predictors. Push λ higher and even x₂ drops, until at large λ only the intercept survives.

lasso is elnet-fit with #:alpha 1.0. The third coefficient comes back exactly 0.0 — the irrelevant predictor has been selected out.