  We propose a semi-supervised generative model, SeGMA, which learns a joint
probability distribution of data and their classes and which is implemented in
a typical Wasserstein auto-encoder framework. We choose a mixture of Gaussians
as a target distribution in latent space, which provides a natural splitting of
data into clusters. To connect Gaussian components with correct classes, we use
a small amount of labeled data and a Gaussian classifier induced by the target
distribution. SeGMA is optimized efficiently due to the use of Cramer-Wold
distance as a maximum mean discrepancy penalty, which yields a closed-form
expression for a mixture of spherical Gaussian components and thus obviates the
need of sampling. While SeGMA preserves all properties of its semi-supervised
predecessors and achieves at least as good generative performance on standard
benchmark data sets, it presents additional features: (a) interpolation between
any pair of points in the latent space produces realistically-looking samples;
(b) combining the interpolation property with disentangled class and style
variables, SeGMA is able to perform a continuous style transfer from one class
to another; (c) it is possible to change the intensity of class characteristics
in a data point by moving the latent representation of the data point away from
specific Gaussian components.
