Active hinge set
= Active hinge set
{title2=$I(x)=\{i:1-a_ix>0\}$}
For a sample term $\max\{0,1-a_ix\}$, the active hinge set contains indices with $1-a_ix>0$. At strict negative margins the hinge is inactive, while zero margins allow fractional <hinge-loss optimality weights>. Away from zero margins, the active set stays fixed on a sufficiently small candidate solution neighborhood.