Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 218 / 2 / c

Coordinate descent cycles through the intercept and coefficient coordinates, minimizing the convex ridge objective in one coordinate while holding the others fixed. Given current coefficients, updateFor coordinate $j$, form the partial residualand update it by the exact one-dimensional minimizerRepeated sweeps converge to the unique fitted value because the objective is a convex function; with $\lambda >0$ it is strictly convex in $\beta$.