Overview of machine learning

The most widely studied problem in machine learning is supervised learning. We are given a labeled training set of input-output pairs, D = (xi, yi)i=1, and have to learn a way to predict the output or target ỹ for a novel test input x̃ (i.e, for x̃ 6∈ D). (We use the tilde notation to denote test cases that we have not seen before.) Some examples include: predicting if someone has cancer ỹ ∈ {0, 1} given some measured variables x̃; predicting the stock price tomorrow ỹ ∈ IR given the stock prices today x̃; etc. A common approach is to just predict one’s “best guess”, such as ŷ(x̃). However, we prefer to compute a probability distribution over the output, p(ỹ|x̃), since it is very useful to have a measure of confidence associated with one’s prediction, especially in medical and financial domains. In addition, probabilistic methods are essential for unsupervised learning, as we discuss in Section 3. If y is discrete or categorical, say y ∈ {1, 2, . . . , C}, this problem is called classification or pattern recognition. If there are C = 2 classes or labels, the problem is called binary classification (see Figure 1 for an example), otherwise it is called multi-class classification. We usually assume the classes are mutually exclusive, so y can only be in one possible state. If we want to allow multiple labels, we can represent y by a bit-vector of length C, so yj = 1 if y belongs to class j. If y is continuous, say y ∈ IR, this problem is called regression. If y is multidimensional, say y ∈ IR , we call it multivariate regression. If y is discrete, but ordered (e.g., y ∈ {low,medium,high}), the problem is called ordinal regression. A priori, our prediction might be quite poor, but we are provided with a labeled training set of input-output pairs, D = (xi, yi) n i=1, which provides a set of examples of the “right response” for a set of possible inputs. If each input