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We propose a semi-supervised generative model, SeGMA, which learns a jointprobability distribution of data and their classes and which is implemented ina typical Wasserstein auto-encoder framework. We choose a mixture of Gaussiansas a target distribution in latent space, which provides a natural splitting ofdata into clusters. To connect Gaussian components with correct classes, we usea small amount of labeled data and a Gaussian classifier induced by the targetdistribution. SeGMA is optimized efficiently due to the use of Cramer-Wolddistance as a maximum mean discrepancy penalty, which yields a closed-formexpression for a mixture of spherical Gaussian components and thus obviates theneed of sampling. While SeGMA preserves all properties of its semi-supervisedpredecessors and achieves at least as good generative performance on standardbenchmark data sets, it presents additional features: (a) interpolation betweenany pair of points in the latent space produces realistically-looking samples;(b) combining the interpolation property with disentangled class and stylevariables, SeGMA is able to perform a continuous style transfer from one classto another; (c) it is possible to change the intensity of class characteristicsin a data point by moving the latent representation of the data point away fromspecific Gaussian components.

SeGMA: Semi-Supervised Gaussian Mixture Auto-Encoder