A type of Machine learning problem where only some of the labels ('outputs') are available in the training data, the rest of the training data being just 'inputs'.
Generative models are often used for Feature learning from the whole input data set, and then using the learned features, a model can be trained with the few labelled samples. See for instance, Generative adversarial networks
I think, Generative supervised learning is sometimes used in the labelled part, and the rest of the trained data is used to train the Generative model of the inputs, using techniques from Unsupervised learning. The latent variables may be seen as predicted outputs for the unlabeled inputs.