Train, validation, and test roles

Problem

A team fits polynomial degrees 11 through 1010. Which split fits the coefficients, which split selects the degree, and when is the test split used? Why does repeatedly selecting models by test performance invalidate the intended estimate?

Reveal answer or reference solution

Fit the coefficients on training data, select the degree on validation data, and use test data once after all choices are fixed. Repeated test-based selection adapts development to accidental test-sample features, causing optimistic selection bias; the score is no longer an untouched generalization estimate.

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