Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network.

The authors develop a framework allowing VAE type computation on a broad class of probablistic model structures. This is motivated in particular by the idea that some lvs may have a straightforward meaning and have some labels available (e.g. which digit in MNIST/SVHN, what lighting direction in the face data), whereas others are more intangible (e.g. They propose a slightly different approach to the semi-supervised VAE of Kingma et al., by considering the (semi)supervised variables y as LVs forced to specific values for the supervised data samples. This is straightforward in the setting where q(y x) can be calculated directly, and can be handled by importance sampling if integration over z is required to calculate q(y x). Experiments are presented on MNIST, SVHN and a faces image data with variation in lighting according 38 individuals.

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Here we are interested in learning disentangled representations that encode distinct aspects of the data into separate variables. We propose to learn such representations using model architectures that generalise from standard VAEs, employing a general graphical model structure in the encoder and decoder. This allows us to train partially-specified models that make relatively strong assumptions about a subset of interpretable variables and rely on the flexibility of neural networks to learn representations for the remaining variables. We further define a general objective for semi-supervised learning in this model class, which can be approximated using an importance sampling procedure.