Error function (modelling)

In the modelling framework the error function determines how good the current model $\hat{f}$ is at fitting the training data $T$. This is a function maps from our parameter space to some evaluation space, usually $\mathbb{R}$ - if we let $o$ be the objective function it normally takes the form

$$E(w) = \sum_{(x,y) \in T} o(f(x), y).$$

Though this depends on our learning method.