Supervised learning
Supervised learning uses examples for which both input variables and desired outputs are known.
A dataset can be written
\[\{(x_i,y_i)\}_{i=1}^{n},\]where \(x_i\) contains features and \(y_i\) is the target. A model \(f(x;\theta)\) is fitted so that its predictions are close to the observed targets.
Two main tasks
Regression predicts a numerical quantity, such as concentration or future case count. Classification predicts a category, such as infected versus uninfected.
Generalisation
The objective is not merely to reproduce training examples but to perform well on relevant new observations.
Key idea. Supervised learning learns an input-to-output relationship from labelled examples and is evaluated by its performance on unseen data.