Cross-Validation and Information Criteria

The ridge/lasso worked example picked $\lambda=5.0$ and $\lambda=0.1$ with no justification beyond "these values work." This note supplies the missing discipline: cross-validation, which estimates test error directly by repeatedly holding out data, and information criteria (AIC, BIC), which estimate it analytically from the training fit alone. Both answer the same question — "how much should I trust a candidate value of $\lambda$, or a candidate model, to generalise?" — the honest version of the train/test protocol from Topic 1, extended to choosing between models rather than just evaluating one.