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.

提出了一种半监督生成模型 SeGMA，它是在典型的 Wasserstein 自编码器框架中实现的，可以有效地进行优化，并在标准基准数据集上达到至少与其半监督前身同样好的生成性能。

SeGMA：半监督高斯混合自编码器

SeGMA: Semi-Supervised Gaussian Mixture Auto-Encoder

We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building
a generative model of the data distribution. WAE minimizes a penalized form of
the Wasserstein distance between the model distribution and the target
distribution, which leads to a different regularizer than the one used by the
Variational Auto-Encoder (VAE). This regularizer encourages the encoded
training distribution to match the prior. We compare our algorithm with several
other techniques and show that it is a generalization of adversarial
auto-encoders (AAE). Our experiments show that WAE shares many of the
properties of VAEs (stable training, encoder-decoder architecture, nice latent
manifold structure) while generating samples of better quality, as measured by
the FID score.

本文提出了 Wasserstein 自编码器（WAE）算法，通过最小化 Wasserstein 距离来构建数据分布的生成模型，并与其他技术进行比较，表明其是对抗自编码器（AAE）的推广，可用于生成更高质量的样本。