Wat is Supervised and unsupervised learning?

Supervised learning fits a function $f_\theta$ from features $x\in\mathbb R^p$ to a target $y$ on examples $(x_i, y_i)$, $i = 1,\dots,n$, by minimising an empirical loss $\mathcal L_n(\theta) = \frac1n\sum_i\ell(y_i, f_\theta(x_i))$, so that $f_\theta$ predicts $y$ for new $x$. Unsupervised learning has no target: it describes the distribution of $x$ itself (clusters, factors, a lower-dimensional representation, a density).