Population Loss

Given a dataset with records $\{x_i, y_i\}$ and a model $\hat y_i = f(x_i)$. Suppose we know the actual generating process of the dataset and the joint probability density distribution of all the data points is $p(x, y)$, the population loss is defined on the whole assumed population,

$$ \begin{align} \mathcal L_{P} = \mathop{\mathbb{E}}_{p(x,y)}[ d(y, f(x))], \end{align} $$

where $d(y, f(x))$ is the distance defined between $y$ and $f(x)$.