Lasso dropout knot (${\gamma }_{\mathrm{drop}}={\min }_{j\in A:-{\beta }_j/d_j>0}(-{\beta }_j/d_j)$)

On a least-angle segment $\beta (\gamma )=\beta +\gamma d$, a nonzero active regression coefficient reaches zero at the displayed first positive root. Continue only as far as the first dropout, inactive-entry event or zero-correlation endpoint. At a dropout remove the vanishing regression coefficient from the active direction and recompute. This preserves agreement between nonzero regression coefficient signs and residual-score signs, which the Karush-Kuhn-Tucker conditions for the Lasso require. A removed regression coefficient may re-enter later; the active set need not grow monotonically.