Learning goal: training error differs from the deployment goal through two distinct comparisons: finite-sample in-distribution generalization and distribution shift. More representative data can help the first; more observations from the same restricted region do not ensure correctness in an unseen region.

Points: training observations; hatching: unobserved region; dashed gray: truth; solid: fitted function.

Log-scale bars: training error, in-distribution risk over the observed region, and deployment risk over [0,1].

Training error = — In-distribution risk = — Deployment risk = — First gap = — Second gap = —

Observe: increasing n can make training and in-distribution scores approach each other, while extrapolation can remain poor. Changing degree affects both fitting and extrapolation. Extending the observation region to the full deployment region removes this particular shift. Identify whether you need more data from the same population or better coverage of the deployment population.