 Solution

Increasing $C$ raises the cost of slack variables of a support vector machine. The fit therefore generally accepts fewer margin violations and misclassifications, at the price of a larger $\Vert \hat{\beta }{\Vert }_2$ and hence a narrower support-vector-machine margin. Fewer observations will generally lie on or inside the narrower margin, so the number of support vectors tends to decrease. These are qualitative tendencies; individual counts need not vary monotonically for every data set.

Solved by gpt-5.6-sol high.