Empirical Loss

An estimation of the Generalization Loss given a Loss Function LL and set EE with a total of NN examples.

EmpLoss⁡L,E(h):=1N(∑(x,y)∈EL(y,h(x)))\operatorname{EmpLoss}_{L, E}(h):=\frac{1}{N}\left(\sum_{(x, y) \in E} L(y, h(x))\right)

We then get the estimated best hypothesis

h^∗:=argmin⁡h∈H EmpLoss L,E(h)\widehat{h}^*:=\underset{h \in \mathcal{H}}{\operatorname{argmin}} \text { EmpLoss }_{L, E}(h)