  Deep generative models trained with large amounts of unlabelled data have
proven to be powerful within the domain of unsupervised learning. Many real
life data sets contain a small amount of labelled data points, that are
typically disregarded when training generative models. We propose the
Cluster-aware Generative Model, that uses unlabelled information to infer a
latent representation that models the natural clustering of the data, and
additional labelled data points to refine this clustering. The generative
performances of the model significantly improve when labelled information is
exploited, obtaining a log-likelihood of -79.38 nats on permutation invariant
MNIST, while also achieving competitive semi-supervised classification
accuracies. The model can also be trained fully unsupervised, and still improve
the log-likelihood performance with respect to related methods.
