Simultaneous Predictive Classification

A framework for predictive classification that treats the test data in a unified fashion in supervised, semi-supervised and unsupervised classification is  introduced. A novel supervised classification principle based on marginalization over test data labels is shown be the optimal classifier under an intuitively attractive utility function. Simultaneous and marginal supervised predictive classifiers are shown to become equivalent classification rules when the amount of training data increases. We also note how the predictive distributions can be factorized with respect to an arbitrary decomposable undirected graph, which can either be given \ a priori  or learned jointly with the classifier from the combined training and test data.