Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 3 / c

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.

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