Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 223 / 2 / c / Solution

For ${\theta }_{\gamma }=(\gamma ,0,\dots ,0{)}^T$, every moved observation has residualEvery original observation hasSelecting any $h$ losses and adding $\lambda \Vert {\theta }_{\gamma }{\Vert }_1=\lambda \gamma$ gives