Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 218 / 4 / a / Solution

For $X_i^{\ast }=(1,X_i^T{)}^T$ and $\gamma =({\gamma }_0,{\beta }^T{)}^T$, a linear support vector machine predictsOne penalized formulation minimizes empirical hinge loss plus a squared Euclidean norm penalty:Conventions often leave the intercept unpenalized, replacing $\Vert \gamma {\Vert }_2^2$ by $\Vert \beta {\Vert }_2^2$; this does not change the role of the two terms.