Interpolators

Definition

Let $(u^1, v^1), \dots , (u^n, v^n)$ be a paired dataset in $\mathcal{U} \times \mathcal{V} $. An interpolator is a predictor $f: \mathcal{U} \to \mathcal{V} $ which satisifes for which

\[ f(u^i) = u^i \]

for each $i = 1 , \dots , n$. In this case we say that the predictor $f$ interpolates the dataset.