where 𝒘 is a vector of parameters and 𝜖 is an unobserved noise term. When 𝒙 𝑖 is multi-dimensional and 𝑦 𝑖 is one-dimensional, the method is referred to as Multiple Linear Regression (MLR). In a non-Bayesian paradigm, our objective is to estimate 𝒘 in such a way that the error between the predicted values 𝑦 ̂𝑖 and the target labels 𝑦 𝑖 is minimized. To make sure that the trained model generalizes to other data points which do not appear in the training set, we can add penalization terms on 𝒘, leading to a Penalized Multiple Linear Regression (PMLR) model. It is worth noting that, for MLR, when we set the minimization objective to be the squared loss between the predicted values and the target labels, i.e.