Wat is Generalisation error, overfitting, bias–variance decomposition?

The generalisation error of a fitted model $\hat f$ is its expected loss on a new draw $(x, y)$ from the distribution the model will meet. Overfitting is the fitting of features of the training sample that do not recur, so that the in-sample loss understates the generalisation error. For the squared loss, the bias–variance decomposition splits the expected generalisation error at a point into noise, squared bias and variance (Proposition 1.4).