Generative or Discriminative? Getting the Best of Both Worlds

For many applications of machine learning the goal is to predict the value of a vector c given the value of a vector x of input features. In a classification problem c represents a discrete class label, whereas in a regression problem it corresponds to one or more continuous variables. From a probabilistic perspective, the goal is to find the conditional distribution p(c|x). The most common approach to this problem is to represent the conditional distribution using a parametric model, and then to determine the parameters using a training set consisting of pairs {xn, cn} of input vectors along with their corresponding target output vectors. The resulting conditional distribution can be used to make predictions of c for new values of x. This is known as a discriminative approach, since the conditional distribution discriminates directly between the different values of c.