An analyst fits ridge and lasso regressions to 200 marketing features. With lasso at the CV-chosen alpha, 176 coefficients are exactly zero. With ridge at its CV-chosen alpha, none are zero but most are small.
Why does lasso produce exact zeros while ridge does not?
Why did you pick that answer? Two or three sentences. The act of articulating it is what builds the judgment — not the click that follows.
The L1 penalty |β| has constant slope, so the optimizer keeps paying the same price for a small coefficient and finds it cheaper to set it to zero. The L2 penalty β² has zero slope at zero, so shrinking a tiny coefficient further saves almost nothing. This is why lasso doubles as automatic feature selection — 24 surviving features are a story a marketing director can read.
Lasso never computes p-values. Zeros come from the geometry of the penalty, not from hypothesis tests.
Alphas are not comparable across penalties. Any ridge alpha short of infinity leaves every coefficient nonzero.
Standardization is needed so the penalty treats features fairly, but it changes scale, not sparsity.