Supervised learning - Classification Actually, in supervised learning, this is simply a task of mapping an input to its corresponding output. That output could take, maybe, an element of a set of classes, one to C. In the case of binary classification, the C will be two, and if in the case of multiclass classification, C will be more than two. C means a class here. In order to formalize the supervised learning task, we have a concept called function approximation. Function approximation is here to play a role in mapping the input to its output. That’s how we assume Y is equal to a function of X. This is the way we map the function. Actually, the function maps X to the corresponding Y. Here, the function f is unknown that is being learned from the past experience, but the goal of f learning is to estimate the function f, given a labeled training set, and then to make predictions using Y = f(X). So, this particular function is giving your probabilistic output. We can always compute the best guess or true best guess, so that the function is maximized to the maximum of the probability. So, Y is always a function of X, which yields the correct label class, which assigns X to the appropriate class C. We can say, maximize the probability of assigning to the class is maximized, or maximize assigning the data to the corresponding class with the probability of P, where Y is assigned to C, given for the given X with respect to the training example D. This is how, actually, the function approximation is used to map input to the output. It is also known as maximum posterior probability (MAP). This is a MAP estimate. The problem is always a posterior problem. We need to maximize the posterior probability. Since this is a posterior probability, this has been written as a conditional probability equation, where Y is assigned to a class, subject to the given X, and the P knowledge D.