Supervised learning algorithms aim to fit a function which maps the input features into predictions based on a training dataset consisting of input-target pairs. In most cases, we assume the relationship between the input features and targets is linear. Say we have a training set of independent input features 𝑿 = {𝒙 1 , 𝒙 2 , … , 𝒙 𝑁 } and target labels 𝒚 = {𝑦 1 , 𝑦 2 , … , 𝑦 𝑁 }. The relationship between 𝑿 and 𝒚 is: