Loss class

Given a hypothesis class $\mathcal{H}$ and a loss function $\ell$, its loss class is the function classIt lets properties of a learning problem be studied through the random fluctuations of the losses themselves.

For a classifier $h$ and a labelled example $z=(x,y)$, the misclassification loss isIt is also called zero-one loss because it is zero for a correct prediction and one for an incorrect prediction.

The misclassification risk of a classifier is its expected misclassification loss,

On labelled examples $Z_1,\dots ,Z_n$, the empirical misclassification risk isAn empirical risk minimizer chooses a classifier attaining the smallest value over its hypothesis class.