Mean squared error (MSE)

The mean squared error is the square of the $l_2$ norm for two points in $B^k$, i.e.

$$mse(x,y) = \frac{1}{k}\sum_{i=1}^k (x_i - y_i)^2.$$

This is normally applied in the context of machine learning to assess models against some testing data $T$. In the modelling framework we would say the

$$mse(\hat{f}, T) = \frac{1}{\vert T \vert} \sum_{(a, b) \in T} (\hat{f}(a) - b)^2.$$