Validation set

A validation set is held out from parameter fitting and used to choose models or tuning parameters. A separate test set is then needed for an unbiased final evaluation after selection.

A test set is held out from both parameter fitting and model selection and is used to estimate the final selected procedure's prediction error. A validation set influences the choice; a test set assesses that choice after it is fixed. The distinction concerns how observations are used, not their file names.

For a fixed rule and an independent test set of size $m$ from the target probability distribution,This test error is an estimate, with sampling uncertainty; it is not a guarantee for each future prediction. Dataset shift changes what performance the estimate represents.

In the overfitting example, all degree choices are fixed in advance, cross-validation uses only training data, and the selected degree is locked before evaluating 400 separate points. Displaying the other curves afterward explains their behavior; it does not authorize selecting by those scores. Repeatedly inspecting a test set and changing the model makes it part of model selection, introducing data leakage and potentially optimistic assessment. ^[ref]