Past exam of the mathematics course of the University of Cambridge 2024 iii Paper 218 2 b Solution Created 2026-09-24 Updated 2026-09-25
Choose to minimize an estimate of out-of-sample mean squared prediction error, commonly K-fold cross-validation or a separate validation set. As increases, the coefficient vector is shrunk toward zero. This generally increases bias of an estimator but decreases variance of an estimator; the minimizing value balances the two contributions in the bias-variance tradeoff. The independent test set in the question can assess the final choice, but repeatedly selecting on that same set would cause data leakage.
Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 218 4 f Solution Created 2026-09-24 Updated 2026-09-25
The assignment
nn.model.i <- nn.model does not construct a fresh untrained Keras model: it aliases an object whose weights were already fitted using every training observation, including the nominally held-out one, and repeated fits continue mutating those weights. This data leakage makes metric2 severely optimistic. Moreover, random leave-one-out validation among reviews from 2012--2025 does not reproduce the dataset shift to new recent reviews that metric1 measures.