  Classifiers for the semi-supervised setting often combine strong supervised
models with additional learning objectives to make use of unlabeled data. This
results in powerful though very complex models that are hard to train and that
demand additional labels for optimal parameter tuning, which are often not
given when labeled data is very sparse. We here study a minimalistic
multi-layer generative neural network for semi-supervised learning in a form
and setting as similar to standard discriminative networks as possible. Based
on normalized Poisson mixtures, we derive compact and local learning and neural
activation rules. Learning and inference in the network can be scaled using
standard deep learning tools for parallelized GPU implementation. With the
single objective of likelihood optimization, both labeled and unlabeled data
are naturally incorporated into learning. Empirical evaluations on standard
benchmarks show, that for datasets with few labels the derived minimalistic
network improves on all classical deep learning approaches and is competitive
with their recent variants without the need of additional labels for parameter
tuning. Furthermore, we find that the studied network is the best performing
monolithic (`non-hybrid') system for few labels, and that it can be applied in
the limit of very few labels, where no other system has been reported to
operate so far.
