Generative, Fully Bayesian, Gaussian, Openset Pattern Classifier

Observable patterns live in R and belong to K different classes. We are given a supervised training database, (X, L), where X represents the training patterns of all the classes and L represents their true class labels. We want to recognize the unknown classes to which new unlabelled test patterns belong. For this purpose we pretend there is a generative model, with unknown parameter Φ, that generates all train and test data. Although Φ is unknown, it is assumed to be the same for train and test. For the purposes of this exercise, we choose perhaps the simplest possible such generative model, which has multivariate normal, class-conditional distributions of the form: