Generative Semi-supervised Classification

We propose a deep generative approach to semi-supervised classification. The proposed approach is based on the idea that learning a conditional class probability function is equivalenttolearningaconditionalgeneratorfunctionfortheconditionalclassprobability. This idea leads to the construction of an objective function for learning a classifier and a conditional class generator that naturally combines the information from both labeled and unlabeled observations. We take advantage of the approximation power of deep neural networks to approximate the classifier and the conditional generator nonparametrically. We establish consistency and convergence properties of the resulting estimators with respect to certain metric under suitable conditions. Moreover, we conduct numerical studies with simulated and real data to evaluate the proposed method and illustrate that the proposed method outperforms several existing semi-supervised classification methods as well as supervised methods trained with only labeled samples, especially when the size of the labeled sample is small.