Intuitions on L1 and L2 Regularisation

L1 and L2 regularisation owes its name to L1 and L2 norm of a vector w respectively. A linear regression model that implements L1 norm for regularisation is called lasso regression, and one that implements (squared) L2 norm for regularisation is called ridge regression. Note: Strictly speaking, the last equation (ridge regression) is a loss function with squared L2 norm of the weights (notice the absence of the square root). The regularisation terms are'constraints' by which an optimisation algorithm must'adhere to' when minimising the loss function, apart from having to minimise the error between the true y and the predicted ŷ. Let's define a model to see how L1 and L2 work.