  Inference and learning for probabilistic generative networks is often very
challenging and typically prevents scalability to as large networks as used for
deep discriminative approaches. To obtain efficiently trainable, large-scale
and well performing generative networks for semi-supervised learning, we here
combine two recent developments: a neural network reformulation of hierarchical
Poisson mixtures (Neural Simpletrons), and a novel truncated variational EM
approach (TV-EM). TV-EM provides theoretical guarantees for learning in
generative networks, and its application to Neural Simpletrons results in
particularly compact, yet approximately optimal, modifications of learning
equations. If applied to standard benchmarks, we empirically find, that
learning converges in fewer EM iterations, that the complexity per EM iteration
is reduced, and that final likelihood values are higher on average. For the
task of classification on data sets with few labels, learning improvements
result in consistently lower error rates if compared to applications without
truncation. Experiments on the MNIST data set herein allow for comparison to
standard and state-of-the-art models in the semi-supervised setting. Further
experiments on the NIST SD19 data set show the scalability of the approach when
a manifold of additional unlabeled data is available.
