Wat is Regularisation, ridge, lasso, elastic net?

Regularisation adds a penalty on the size of the coefficients to the least-squares objective. Ridge regression minimises $\lvert y - X\beta\rvert^2 + \lambda\lvert\beta\rvert_2^2$; the lasso minimises $\frac1{2n}\lvert y - X\beta\rvert^2 + \lambda\lvert\beta\rvert_1$; the elastic net uses the penalty $\lambda\bigl(\alpha\lvert\beta\rvert_1 + \frac{1 - \alpha}2\lvert\beta\rvert_2^2\bigr)$, $\alpha \in [0, 1]$.